Fix compilation
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304
stdPreamble.tex
304
stdPreamble.tex
@ -17,10 +17,6 @@
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\usepackage{graphicx}
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\usepackage{tikz}
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% von Jakob
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\usepackage{caption}
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\usepackage{subcaption}
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% Font packages
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\usepackage{mathrsfs}
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@ -59,129 +55,135 @@
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%
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% Input characters
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%
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\newunicodechar{α}{\ensuremath{α}}
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\newunicodechar{β}{\ensuremath{β}}
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\newunicodechar{χ}{\ensuremath{χ}}
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\newunicodechar{δ}{\ensuremath{δ}}
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\newunicodechar{ε}{\ensuremath{ε}}
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\newunicodechar{Δ}{\ensuremath{Δ}}
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\newunicodechar{η}{\ensuremath{η}}
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\newunicodechar{γ}{\ensuremath{γ}}
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\newunicodechar{Γ}{\ensuremath{Γ}}
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\newunicodechar{ι}{\ensuremath{ι}}
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\newunicodechar{κ}{\ensuremath{κ}}
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\newunicodechar{λ}{\ensuremath{λ}}
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\newunicodechar{Λ}{\ensuremath{Λ}}
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\newunicodechar{ν}{\ensuremath{ν}}
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\newunicodechar{μ}{\ensuremath{μ}}
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\newunicodechar{ω}{\ensuremath{ω}}
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\newunicodechar{Ω}{\ensuremath{Ω}}
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\newunicodechar{π}{\ensuremath{π}}
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\newunicodechar{Π}{\ensuremath{\Pi}}
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\newunicodechar{φ}{\ensuremath{φ}}
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\newunicodechar{Φ}{\ensuremath{Φ}}
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\newunicodechar{ψ}{\ensuremath{ψ}}
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\newunicodechar{Ψ}{\ensuremath{Ψ}}
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\newunicodechar{ρ}{\ensuremath{ρ}}
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\newunicodechar{σ}{\ensuremath{σ}}
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\newunicodechar{Σ}{\ensuremath{Σ}}
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\newunicodechar{τ}{\ensuremath{τ}}
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\newunicodechar{θ}{\ensuremath{θ}}
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\newunicodechar{Θ}{\ensuremath{Θ}}
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\newunicodechar{ξ}{\ensuremath{ξ}}
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\newunicodechar{Ξ}{\ensuremath{Ξ}}
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\newunicodechar{ζ}{\ensuremath{ζ}}
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\newunicodechar{ℓ}{\ensuremath{ℓ}}
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\newunicodechar{א}{\ensuremath{\aleph}}
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\newunicodechar{α}{\ensuremath{\alpha}}
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\newunicodechar{β}{\ensuremath{\beta}}
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\newunicodechar{χ}{\ensuremath{\chi}}
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\newunicodechar{δ}{\ensuremath{\delta}}
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\newunicodechar{ε}{\ensuremath{\varepsilon}}
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\newunicodechar{Δ}{\ensuremath{\Delta}}
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\newunicodechar{η}{\ensuremath{\eta}}
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\newunicodechar{γ}{\ensuremath{\gamma}}
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\newunicodechar{Γ}{\ensuremath{\Gamma}}
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\newunicodechar{ι}{\ensuremath{\iota}}
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\newunicodechar{κ}{\ensuremath{\kappa}}
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\newunicodechar{λ}{\ensuremath{\lambda}}
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\newunicodechar{Λ}{\ensuremath{\Lambda}}
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\newunicodechar{ν}{\ensuremath{\nu}}
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\newunicodechar{μ}{\ensuremath{\mu}}
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\newunicodechar{ω}{\ensuremath{\omega}}
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\newunicodechar{Ω}{\ensuremath{\Omega}}
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\newunicodechar{π}{\ensuremath{\pi}}
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\newunicodechar{Π}{\ensuremath{\Pi}}
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\newunicodechar{φ}{\ensuremath{\phi}}
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\newunicodechar{Φ}{\ensuremath{\Phi}}
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\newunicodechar{ψ}{\ensuremath{\psi}}
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\newunicodechar{Ψ}{\ensuremath{\Psi}}
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\newunicodechar{ρ}{\ensuremath{\rho}}
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\newunicodechar{σ}{\ensuremath{\sigma}}
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\newunicodechar{Σ}{\ensuremath{\Sigma}}
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\newunicodechar{τ}{\ensuremath{\tau}}
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\newunicodechar{θ}{\ensuremath{\theta}}
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\newunicodechar{Θ}{\ensuremath{\Theta}}
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\newunicodechar{ξ}{\ensuremath{\xi}}
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\newunicodechar{Ξ}{\ensuremath{\Xi}}
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\newunicodechar{ζ}{\ensuremath{\zeta}}
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\newunicodechar{ℓ}{\ensuremath{\ell}}
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\newunicodechar{ï}{\"{\i}}
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\newunicodechar{𝔸}{\ensuremath{𝔸}}
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\newunicodechar{𝔹}{\ensuremath{𝔹}}
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\newunicodechar{ℂ}{\ensuremath{ℂ}}
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\newunicodechar{𝔻}{\ensuremath{𝔻}}
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\newunicodechar{𝔼}{\ensuremath{𝔼}}
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\newunicodechar{𝔽}{\ensuremath{𝔽}}
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\newunicodechar{ℕ}{\ensuremath{ℕ}}
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\newunicodechar{ℙ}{\ensuremath{ℙ}}
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\newunicodechar{ℚ}{\ensuremath{ℚ}}
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\newunicodechar{ℝ}{\ensuremath{ℝ}}
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\newunicodechar{𝕏}{\ensuremath{𝕏}}
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\newunicodechar{ℤ}{\ensuremath{ℤ}}
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\newunicodechar{𝒜}{\ensuremath{𝒜}}
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\newunicodechar{ℬ}{\ensuremath{ℬ}}
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\newunicodechar{𝒞}{\ensuremath{𝒞}}
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\newunicodechar{𝒟}{\ensuremath{𝒟}}
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\newunicodechar{ℰ}{\ensuremath{ℰ}}
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\newunicodechar{ℱ}{\ensuremath{ℱ}}
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\newunicodechar{𝒢}{\ensuremath{𝒢}}
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\newunicodechar{ℋ}{\ensuremath{ℋ}}
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\newunicodechar{𝒥}{\ensuremath{𝒥}}
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\newunicodechar{ℒ}{\ensuremath{ℒ}}
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\newunicodechar{𝒪}{\ensuremath{𝒪}}
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\newunicodechar{𝒬}{\ensuremath{𝒬}}
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\newunicodechar{𝒯}{\ensuremath{𝒯}}
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\newunicodechar{𝒲}{\ensuremath{𝒲}}
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\newunicodechar{𝔸}{\ensuremath{\bA}}
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\newunicodechar{𝔹}{\ensuremath{\bB}}
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\newunicodechar{ℂ}{\ensuremath{\bC}}
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\newunicodechar{𝔻}{\ensuremath{\bD}}
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\newunicodechar{𝔼}{\ensuremath{\bE}}
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\newunicodechar{𝔽}{\ensuremath{\bF}}
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\newunicodechar{𝔾}{\ensuremath{\bG}}
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\newunicodechar{ℕ}{\ensuremath{\bN}}
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\newunicodechar{ℙ}{\ensuremath{\bP}}
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\newunicodechar{ℚ}{\ensuremath{\bQ}}
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\newunicodechar{ℝ}{\ensuremath{\bR}}
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\newunicodechar{𝕏}{\ensuremath{\bX}}
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\newunicodechar{ℤ}{\ensuremath{\bZ}}
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\newunicodechar{𝒜}{\ensuremath{\sA}}
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\newunicodechar{ℬ}{\ensuremath{\sB}}
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\newunicodechar{𝒞}{\ensuremath{\sC}}
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\newunicodechar{𝒟}{\ensuremath{\sD}}
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\newunicodechar{ℰ}{\ensuremath{\sE}}
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\newunicodechar{ℱ}{\ensuremath{\sF}}
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\newunicodechar{𝒢}{\ensuremath{\sG}}
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\newunicodechar{ℋ}{\ensuremath{\sH}}
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\newunicodechar{𝒥}{\ensuremath{\sJ}}
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\newunicodechar{ℒ}{\ensuremath{\sL}}
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\newunicodechar{ℳ}{\ensuremath{\sM}}
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\newunicodechar{𝒪}{\ensuremath{\sO}}
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\newunicodechar{𝒬}{\ensuremath{\sQ}}
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\newunicodechar{𝒮}{\ensuremath{\sS}}
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\newunicodechar{𝒯}{\ensuremath{\sT}}
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\newunicodechar{𝒲}{\ensuremath{\sW}}
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\newunicodechar{∂}{\ensuremath{∂}}
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\newunicodechar{∇}{\ensuremath{∇}}
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\newunicodechar{∂}{\ensuremath{\partial}}
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\newunicodechar{∇}{\ensuremath{\nabla}}
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\newunicodechar{↺}{\ensuremath{↺}}
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\newunicodechar{∞}{\ensuremath{∞}}
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\newunicodechar{⊕}{\ensuremath{⊕}}
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\newunicodechar{⊗}{\ensuremath{⊗}}
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\newunicodechar{•}{\ensuremath{•}}
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\newunicodechar{Λ}{\ensuremath{Λ}}
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\newunicodechar{↪}{\ensuremath{↪}}
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\newunicodechar{→}{\ensuremath{→}}
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\newunicodechar{↦}{\ensuremath{↦}}
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\newunicodechar{⨯}{\ensuremath{⨯}}
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\newunicodechar{∪}{\ensuremath{∪}}
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\newunicodechar{∩}{\ensuremath{∩}}
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\newunicodechar{⊋}{\ensuremath{⊋}}
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\newunicodechar{⊇}{\ensuremath{⊇}}
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\newunicodechar{⊃}{\ensuremath{⊃}}
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\newunicodechar{⊊}{\ensuremath{⊊}}
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\newunicodechar{⊆}{\ensuremath{⊆}}
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\newunicodechar{⊂}{\ensuremath{⊂}}
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\newunicodechar{⊄}{\ensuremath{⊄}}
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\newunicodechar{≥}{\ensuremath{≥}}
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\newunicodechar{≠}{\ensuremath{≠}}
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\newunicodechar{≫}{\ensuremath{≫}}
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\newunicodechar{≪}{\ensuremath{≪}}
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\newunicodechar{↺}{\ensuremath{\circlearrowleft}}
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\newunicodechar{∞}{\ensuremath{\infty}}
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\newunicodechar{⊕}{\ensuremath{\oplus}}
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\newunicodechar{⊗}{\ensuremath{\otimes}}
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\newunicodechar{•}{\ensuremath{\bullet}}
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\newunicodechar{Λ}{\ensuremath{\wedge}}
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\newunicodechar{↪}{\ensuremath{\into}}
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\newunicodechar{→}{\ensuremath{\to}}
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\newunicodechar{↦}{\ensuremath{\mapsto}}
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\newunicodechar{⨯}{\ensuremath{\times}}
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\newunicodechar{∪}{\ensuremath{\cup}}
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\newunicodechar{∩}{\ensuremath{\cap}}
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\newunicodechar{⊋}{\ensuremath{\supsetneq}}
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\newunicodechar{⊇}{\ensuremath{\supseteq}}
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\newunicodechar{⊃}{\ensuremath{\supset}}
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\newunicodechar{⊊}{\ensuremath{\subsetneq}}
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\newunicodechar{⊆}{\ensuremath{\subseteq}}
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\newunicodechar{⊂}{\ensuremath{\subset}}
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\newunicodechar{⊄}{\ensuremath{\not \subset}}
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\newunicodechar{≥}{\ensuremath{\geq}}
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\newunicodechar{≠}{\ensuremath{\neq}}
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\newunicodechar{≫}{\ensuremath{\gg}}
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\newunicodechar{≪}{\ensuremath{\ll}}
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\newunicodechar{≤}{\ensuremath{≤}}
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\newunicodechar{∈}{\ensuremath{∈}}
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\newunicodechar{∉}{\ensuremath{\not ∈}}
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\newunicodechar{∖}{\ensuremath{∖}}
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\newunicodechar{◦}{\ensuremath{◦}}
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\newunicodechar{°}{\ensuremath{°}}
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\newunicodechar{≤}{\ensuremath{\leq}}
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\newunicodechar{∈}{\ensuremath{\in}}
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\newunicodechar{∉}{\ensuremath{\not \in}}
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\newunicodechar{∖}{\ensuremath{\setminus}}
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\newunicodechar{◦}{\ensuremath{\circ}}
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\newunicodechar{°}{\ensuremath{^\circ}}
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\newunicodechar{…}{\ifmmode\mathellipsis\else\textellipsis\fi}
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\newunicodechar{·}{\ensuremath{·}}
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\newunicodechar{⋯}{\ensuremath{⋯}}
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\newunicodechar{∅}{\ensuremath{∅}}
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\newunicodechar{⇒}{\ensuremath{⇒}}
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\newunicodechar{·}{\ensuremath{\cdot}}
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\newunicodechar{⋯}{\ensuremath{\cdots}}
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\newunicodechar{∅}{\ensuremath{\emptyset}}
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\newunicodechar{⇒}{\ensuremath{\Rightarrow}}
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\newunicodechar{⁰}{\ensuremath{⁰}}
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\newunicodechar{¹}{\ensuremath{¹}}
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\newunicodechar{²}{\ensuremath{²}}
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\newunicodechar{³}{\ensuremath{³}}
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\newunicodechar{⁴}{\ensuremath{⁴}}
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\newunicodechar{⁵}{\ensuremath{⁵}}
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\newunicodechar{⁶}{\ensuremath{⁶}}
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\newunicodechar{⁷}{\ensuremath{⁷}}
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\newunicodechar{⁸}{\ensuremath{⁸}}
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\newunicodechar{⁹}{\ensuremath{⁹}}
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\newunicodechar{ⁱ}{\ensuremath{ⁱ}}
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\newunicodechar{⁰}{\ensuremath{^0}}
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\newunicodechar{¹}{\ensuremath{^1}}
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\newunicodechar{²}{\ensuremath{^2}}
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\newunicodechar{³}{\ensuremath{^3}}
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\newunicodechar{⁴}{\ensuremath{^4}}
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\newunicodechar{⁵}{\ensuremath{^5}}
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\newunicodechar{⁶}{\ensuremath{^6}}
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\newunicodechar{⁷}{\ensuremath{^7}}
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\newunicodechar{⁸}{\ensuremath{^8}}
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\newunicodechar{⁹}{\ensuremath{^9}}
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\newunicodechar{ⁱ}{\ensuremath{^i}}
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\newunicodechar{⁺}{\ensuremath{^+}}
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\newunicodechar{⌈}{\ensuremath{⌈}}
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\newunicodechar{⌉}{\ensuremath{⌉}}
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\newunicodechar{⌊}{\ensuremath{⌊}}
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\newunicodechar{⌋}{\ensuremath{⌋}}
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\newunicodechar{⌈}{\ensuremath{\lceil}}
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\newunicodechar{⌉}{\ensuremath{\rceil}}
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\newunicodechar{⌊}{\ensuremath{\lfloor}}
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\newunicodechar{⌋}{\ensuremath{\rfloor}}
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\newunicodechar{≅}{\ensuremath{≅}}
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\newunicodechar{⇔}{\ensuremath{⇔}}
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\newunicodechar{∃}{\ensuremath{∃}}
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\newunicodechar{±}{\ensuremath{±}}
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\newunicodechar{≅}{\ensuremath{\cong}}
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\newunicodechar{⇔}{\ensuremath{\Leftrightarrow}}
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\newunicodechar{∃}{\ensuremath{\exists}}
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\newunicodechar{±}{\ensuremath{\pm}}
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%
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@ -227,7 +229,7 @@
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\DeclareMathOperator{\red}{red}
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\DeclareMathOperator{\reg}{reg}
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\DeclareMathOperator{\sat}{sat}
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\DeclareMathOperator{\sEnd}{ℰ\negthinspace \mathit{nd}}
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\DeclareMathOperator{\sEnd}{\sE\negthinspace \mathit{nd}}
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\DeclareMathOperator{\sing}{sing}
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\DeclareMathOperator{\Spec}{Spec}
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\DeclareMathOperator{\Sym}{Sym}
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@ -237,30 +239,30 @@
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\DeclareMathOperator{\Frob}{Frob}
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% Sheaves
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\newcommand{𝒜}{\scr{A}}
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\newcommand{ℬ}{\scr{B}}
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\newcommand{𝒞}{\scr{C}}
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\newcommand{𝒟}{\scr{D}}
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\newcommand{ℰ}{\scr{E}}
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\newcommand{ℱ}{\scr{F}}
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\newcommand{𝒢}{\scr{G}}
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\newcommand{ℋ}{\scr{H}}
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\newcommand{\sA}{\scr{A}}
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\newcommand{\sB}{\scr{B}}
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\newcommand{\sC}{\scr{C}}
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\newcommand{\sD}{\scr{D}}
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\newcommand{\sE}{\scr{E}}
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\newcommand{\sF}{\scr{F}}
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\newcommand{\sG}{\scr{G}}
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\newcommand{\sH}{\scr{H}}
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\newcommand{\sHom}{\scr{H}\negthinspace om}
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\newcommand{\sI}{\scr{I}}
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\newcommand{𝒥}{\scr{J}}
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\newcommand{\sJ}{\scr{J}}
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\newcommand{\sK}{\scr{K}}
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\newcommand{ℒ}{\scr{L}}
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\newcommand{ℳ}{\scr{M}}
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\newcommand{\sL}{\scr{L}}
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\newcommand{\sM}{\scr{M}}
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\newcommand{\sN}{\scr{N}}
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\newcommand{𝒪}{\scr{O}}
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\newcommand{\sO}{\scr{O}}
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\newcommand{\sP}{\scr{P}}
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\newcommand{𝒬}{\scr{Q}}
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\newcommand{\sQ}{\scr{Q}}
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\newcommand{\sR}{\scr{R}}
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\newcommand{𝒮}{\scr{S}}
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\newcommand{𝒯}{\scr{T}}
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\newcommand{\sS}{\scr{S}}
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\newcommand{\sT}{\scr{T}}
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\newcommand{\sU}{\scr{U}}
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\newcommand{\sV}{\scr{V}}
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\newcommand{𝒲}{\scr{W}}
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\newcommand{\sW}{\scr{W}}
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\newcommand{\sX}{\scr{X}}
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\newcommand{\sY}{\scr{Y}}
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\newcommand{\sZ}{\scr{Z}}
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@ -275,32 +277,32 @@
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\newcommand{\cV}{\mathcal V}
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% Blackboard Bold Symbols
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\newcommand{𝔸}{\mathbb{A}}
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\newcommand{𝔹}{\mathbb{B}}
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\newcommand{ℂ}{\mathbb{C}}
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\newcommand{𝔻}{\mathbb{D}}
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\newcommand{𝔼}{\mathbb{E}}
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\newcommand{𝔽}{\mathbb{F}}
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\newcommand{𝔾}{\mathbb{G}}
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\newcommand{\bA}{\mathbb{A}}
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\newcommand{\bB}{\mathbb{B}}
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\newcommand{\bC}{\mathbb{C}}
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\newcommand{\bD}{\mathbb{D}}
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\newcommand{\bE}{\mathbb{E}}
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\newcommand{\bF}{\mathbb{F}}
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\newcommand{\bG}{\mathbb{G}}
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\newcommand{\bH}{\mathbb{H}}
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\newcommand{\bI}{\mathbb{I}}
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\newcommand{\bJ}{\mathbb{J}}
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\newcommand{\bK}{\mathbb{K}}
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\newcommand{\bL}{\mathbb{L}}
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\newcommand{\bM}{\mathbb{M}}
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\newcommand{ℕ}{\mathbb{N}}
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\newcommand{\bN}{\mathbb{N}}
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\newcommand{\bO}{\mathbb{O}}
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\newcommand{ℙ}{\mathbb{P}}
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\newcommand{ℚ}{\mathbb{Q}}
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\newcommand{ℝ}{\mathbb{R}}
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\newcommand{\bP}{\mathbb{P}}
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\newcommand{\bQ}{\mathbb{Q}}
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\newcommand{\bR}{\mathbb{R}}
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\newcommand{\bS}{\mathbb{S}}
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\newcommand{\bT}{\mathbb{T}}
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\newcommand{\bU}{\mathbb{U}}
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\newcommand{\bV}{\mathbb{V}}
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\newcommand{\bW}{\mathbb{W}}
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\newcommand{𝕏}{\mathbb{X}}
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\newcommand{\bX}{\mathbb{X}}
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\newcommand{\bY}{\mathbb{Y}}
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\newcommand{ℤ}{\mathbb{Z}}
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\newcommand{\bZ}{\mathbb{Z}}
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% Sans serif symbols
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\newcommand{\aB}{{\sf B}}
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@ -343,15 +345,15 @@
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\newtheorem{setting}[thm]{Setting}
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\newtheorem{warning}[thm]{Warning}
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% Numbering of equations. Number equation subordniate to theorems.
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% Numbering of equations. Number equation subordniate to theorems.
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\numberwithin{equation}{thm}
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% Style for enumerated lists. The following makes sure that enumerated lists are
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% Style for enumerated lists. The following makes sure that enumerated lists are
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% numbered in the same way as equations are.
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\setlist[enumerate]{label=(\thethm.\arabic*), before={\setcounter{enumi}{\value{equation}}}, after={\setcounter{equation}{\value{enumi}}}}
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% Shorthand notations
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\newcommand{↪}{↪}
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\newcommand{\into}{\hookrightarrow}
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\newcommand{\onto}{\twoheadrightarrow}
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\newcommand{\wtilde}{\widetilde}
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\newcommand{\what}{\widehat}
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@ -374,4 +376,4 @@
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\newcommand\CounterStep{\addtocounter{thm}{1}\setcounter{equation}{0}}
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% factor - quotient groups
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\newcommand{\factor}[2]{\left. \raise 2pt\hbox{$#1$} \right/\hskip -2pt\raise -2pt\hbox{$#2$}}
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\newcommand{\factor}[2]{\left. \raise 2pt\hbox{$#1$} \right/\hskip -2pt\raise -2pt\hbox{$#2$}}
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