From d60b7d8de5a6db21421613c6392609aa8ce9daec Mon Sep 17 00:00:00 2001
From: Stefan Kebekus <kebekus@users.noreply.github.com>
Date: Thu, 24 Apr 2025 11:06:01 +0200
Subject: [PATCH] Fix compilation

---
 stdPreamble.tex | 304 ++++++++++++++++++++++++------------------------
 1 file changed, 153 insertions(+), 151 deletions(-)

diff --git a/stdPreamble.tex b/stdPreamble.tex
index a83517f..ad4b8cf 100644
--- a/stdPreamble.tex
+++ b/stdPreamble.tex
@@ -17,10 +17,6 @@
 \usepackage{graphicx}
 \usepackage{tikz}
 
-% von Jakob
-\usepackage{caption}
-\usepackage{subcaption}
-
 
 % Font packages
 \usepackage{mathrsfs}
@@ -59,129 +55,135 @@
 %
 % Input characters
 %
-\newunicodechar{α}{\ensuremath{α}}
-\newunicodechar{β}{\ensuremath{β}}
-\newunicodechar{χ}{\ensuremath{χ}}
-\newunicodechar{δ}{\ensuremath{δ}}
-\newunicodechar{ε}{\ensuremath{ε}}
-\newunicodechar{Δ}{\ensuremath{Δ}}
-\newunicodechar{η}{\ensuremath{η}}
-\newunicodechar{γ}{\ensuremath{γ}}
-\newunicodechar{Γ}{\ensuremath{Γ}}
-\newunicodechar{ι}{\ensuremath{ι}}
-\newunicodechar{κ}{\ensuremath{κ}}
-\newunicodechar{λ}{\ensuremath{λ}}
-\newunicodechar{Λ}{\ensuremath{Λ}}
-\newunicodechar{ν}{\ensuremath{ν}}
-\newunicodechar{μ}{\ensuremath{μ}}
-\newunicodechar{ω}{\ensuremath{ω}}
-\newunicodechar{Ω}{\ensuremath{Ω}}
-\newunicodechar{π}{\ensuremath{π}}
-\newunicodechar{Π}{\ensuremath{\Pi}}
-\newunicodechar{φ}{\ensuremath{φ}}
-\newunicodechar{Φ}{\ensuremath{Φ}}
-\newunicodechar{ψ}{\ensuremath{ψ}}
-\newunicodechar{Ψ}{\ensuremath{Ψ}}
-\newunicodechar{ρ}{\ensuremath{ρ}}
-\newunicodechar{σ}{\ensuremath{σ}}
-\newunicodechar{Σ}{\ensuremath{Σ}}
-\newunicodechar{τ}{\ensuremath{τ}}
-\newunicodechar{θ}{\ensuremath{θ}}
-\newunicodechar{Θ}{\ensuremath{Θ}}
-\newunicodechar{ξ}{\ensuremath{ξ}}
-\newunicodechar{Ξ}{\ensuremath{Ξ}}
-\newunicodechar{ζ}{\ensuremath{ζ}}
 
-\newunicodechar{ℓ}{\ensuremath{ℓ}}
+\newunicodechar{א}{\ensuremath{\aleph}}
+\newunicodechar{α}{\ensuremath{\alpha}}
+\newunicodechar{β}{\ensuremath{\beta}}
+\newunicodechar{χ}{\ensuremath{\chi}}
+\newunicodechar{δ}{\ensuremath{\delta}}
+\newunicodechar{ε}{\ensuremath{\varepsilon}}
+\newunicodechar{Δ}{\ensuremath{\Delta}}
+\newunicodechar{η}{\ensuremath{\eta}}
+\newunicodechar{γ}{\ensuremath{\gamma}}
+\newunicodechar{Γ}{\ensuremath{\Gamma}}
+\newunicodechar{ι}{\ensuremath{\iota}}
+\newunicodechar{κ}{\ensuremath{\kappa}}
+\newunicodechar{λ}{\ensuremath{\lambda}}
+\newunicodechar{Λ}{\ensuremath{\Lambda}}
+\newunicodechar{ν}{\ensuremath{\nu}}
+\newunicodechar{μ}{\ensuremath{\mu}}
+\newunicodechar{ω}{\ensuremath{\omega}}
+\newunicodechar{Ω}{\ensuremath{\Omega}}
+\newunicodechar{π}{\ensuremath{\pi}}
+\newunicodechar{Π}{\ensuremath{\Pi}}
+\newunicodechar{φ}{\ensuremath{\phi}}
+\newunicodechar{Φ}{\ensuremath{\Phi}}
+\newunicodechar{ψ}{\ensuremath{\psi}}
+\newunicodechar{Ψ}{\ensuremath{\Psi}}
+\newunicodechar{ρ}{\ensuremath{\rho}}
+\newunicodechar{σ}{\ensuremath{\sigma}}
+\newunicodechar{Σ}{\ensuremath{\Sigma}}
+\newunicodechar{τ}{\ensuremath{\tau}}
+\newunicodechar{θ}{\ensuremath{\theta}}
+\newunicodechar{Θ}{\ensuremath{\Theta}}
+\newunicodechar{ξ}{\ensuremath{\xi}}
+\newunicodechar{Ξ}{\ensuremath{\Xi}}
+\newunicodechar{ζ}{\ensuremath{\zeta}}
+
+\newunicodechar{ℓ}{\ensuremath{\ell}}
 \newunicodechar{ï}{\"{\i}}
 
-\newunicodechar{𝔸}{\ensuremath{𝔸}}
-\newunicodechar{𝔹}{\ensuremath{𝔹}}
-\newunicodechar{ℂ}{\ensuremath{ℂ}}
-\newunicodechar{𝔻}{\ensuremath{𝔻}}
-\newunicodechar{𝔼}{\ensuremath{𝔼}}
-\newunicodechar{𝔽}{\ensuremath{𝔽}}
-\newunicodechar{ℕ}{\ensuremath{ℕ}}
-\newunicodechar{ℙ}{\ensuremath{ℙ}}
-\newunicodechar{ℚ}{\ensuremath{ℚ}}
-\newunicodechar{ℝ}{\ensuremath{ℝ}}
-\newunicodechar{𝕏}{\ensuremath{𝕏}}
-\newunicodechar{ℤ}{\ensuremath{ℤ}}
-\newunicodechar{𝒜}{\ensuremath{𝒜}}
-\newunicodechar{ℬ}{\ensuremath{ℬ}}
-\newunicodechar{𝒞}{\ensuremath{𝒞}}
-\newunicodechar{𝒟}{\ensuremath{𝒟}}
-\newunicodechar{ℰ}{\ensuremath{ℰ}}
-\newunicodechar{ℱ}{\ensuremath{ℱ}}
-\newunicodechar{𝒢}{\ensuremath{𝒢}}
-\newunicodechar{ℋ}{\ensuremath{ℋ}}
-\newunicodechar{𝒥}{\ensuremath{𝒥}}
-\newunicodechar{ℒ}{\ensuremath{ℒ}}
-\newunicodechar{𝒪}{\ensuremath{𝒪}}
-\newunicodechar{𝒬}{\ensuremath{𝒬}}
-\newunicodechar{𝒯}{\ensuremath{𝒯}}
-\newunicodechar{𝒲}{\ensuremath{𝒲}}
+\newunicodechar{𝔸}{\ensuremath{\bA}}
+\newunicodechar{𝔹}{\ensuremath{\bB}}
+\newunicodechar{ℂ}{\ensuremath{\bC}}
+\newunicodechar{𝔻}{\ensuremath{\bD}}
+\newunicodechar{𝔼}{\ensuremath{\bE}}
+\newunicodechar{𝔽}{\ensuremath{\bF}}
+\newunicodechar{𝔾}{\ensuremath{\bG}}
+\newunicodechar{ℕ}{\ensuremath{\bN}}
+\newunicodechar{ℙ}{\ensuremath{\bP}}
+\newunicodechar{ℚ}{\ensuremath{\bQ}}
+\newunicodechar{ℝ}{\ensuremath{\bR}}
+\newunicodechar{𝕏}{\ensuremath{\bX}}
+\newunicodechar{ℤ}{\ensuremath{\bZ}}
+\newunicodechar{𝒜}{\ensuremath{\sA}}
+\newunicodechar{ℬ}{\ensuremath{\sB}}
+\newunicodechar{𝒞}{\ensuremath{\sC}}
+\newunicodechar{𝒟}{\ensuremath{\sD}}
+\newunicodechar{ℰ}{\ensuremath{\sE}}
+\newunicodechar{ℱ}{\ensuremath{\sF}}
+\newunicodechar{𝒢}{\ensuremath{\sG}}
+\newunicodechar{ℋ}{\ensuremath{\sH}}
+\newunicodechar{𝒥}{\ensuremath{\sJ}}
+\newunicodechar{ℒ}{\ensuremath{\sL}}
+\newunicodechar{ℳ}{\ensuremath{\sM}}
+\newunicodechar{𝒪}{\ensuremath{\sO}}
+\newunicodechar{𝒬}{\ensuremath{\sQ}}
+\newunicodechar{𝒮}{\ensuremath{\sS}}
+\newunicodechar{𝒯}{\ensuremath{\sT}}
+\newunicodechar{𝒲}{\ensuremath{\sW}}
 
-\newunicodechar{∂}{\ensuremath{∂}}
-\newunicodechar{∇}{\ensuremath{∇}}
+\newunicodechar{∂}{\ensuremath{\partial}}
+\newunicodechar{∇}{\ensuremath{\nabla}}
 
-\newunicodechar{↺}{\ensuremath{↺}}
-\newunicodechar{∞}{\ensuremath{∞}}
-\newunicodechar{⊕}{\ensuremath{⊕}}
-\newunicodechar{⊗}{\ensuremath{⊗}}
-\newunicodechar{•}{\ensuremath{•}}
-\newunicodechar{Λ}{\ensuremath{Λ}}
-\newunicodechar{↪}{\ensuremath{↪}}
-\newunicodechar{→}{\ensuremath{→}}
-\newunicodechar{↦}{\ensuremath{↦}}
-\newunicodechar{⨯}{\ensuremath{⨯}}
-\newunicodechar{∪}{\ensuremath{∪}}
-\newunicodechar{∩}{\ensuremath{∩}}
-\newunicodechar{⊋}{\ensuremath{⊋}}
-\newunicodechar{⊇}{\ensuremath{⊇}}
-\newunicodechar{⊃}{\ensuremath{⊃}}
-\newunicodechar{⊊}{\ensuremath{⊊}}
-\newunicodechar{⊆}{\ensuremath{⊆}}
-\newunicodechar{⊂}{\ensuremath{⊂}}
-\newunicodechar{⊄}{\ensuremath{⊄}}
-\newunicodechar{≥}{\ensuremath{≥}}
-\newunicodechar{≠}{\ensuremath{≠}}
-\newunicodechar{≫}{\ensuremath{≫}}
-\newunicodechar{≪}{\ensuremath{≪}}
+\newunicodechar{↺}{\ensuremath{\circlearrowleft}}
+\newunicodechar{∞}{\ensuremath{\infty}}
+\newunicodechar{⊕}{\ensuremath{\oplus}}
+\newunicodechar{⊗}{\ensuremath{\otimes}}
+\newunicodechar{•}{\ensuremath{\bullet}}
+\newunicodechar{Λ}{\ensuremath{\wedge}}
+\newunicodechar{↪}{\ensuremath{\into}}
+\newunicodechar{→}{\ensuremath{\to}}
+\newunicodechar{↦}{\ensuremath{\mapsto}}
+\newunicodechar{⨯}{\ensuremath{\times}}
+\newunicodechar{∪}{\ensuremath{\cup}}
+\newunicodechar{∩}{\ensuremath{\cap}}
+\newunicodechar{⊋}{\ensuremath{\supsetneq}}
+\newunicodechar{⊇}{\ensuremath{\supseteq}}
+\newunicodechar{⊃}{\ensuremath{\supset}}
+\newunicodechar{⊊}{\ensuremath{\subsetneq}}
+\newunicodechar{⊆}{\ensuremath{\subseteq}}
+\newunicodechar{⊂}{\ensuremath{\subset}}
+\newunicodechar{⊄}{\ensuremath{\not \subset}}
+\newunicodechar{≥}{\ensuremath{\geq}}
+\newunicodechar{≠}{\ensuremath{\neq}}
+\newunicodechar{≫}{\ensuremath{\gg}}
+\newunicodechar{≪}{\ensuremath{\ll}}
 
-\newunicodechar{≤}{\ensuremath{≤}}
-\newunicodechar{∈}{\ensuremath{∈}}
-\newunicodechar{∉}{\ensuremath{\not ∈}}
-\newunicodechar{∖}{\ensuremath{∖}}
-\newunicodechar{◦}{\ensuremath{◦}}
-\newunicodechar{°}{\ensuremath{°}}
+\newunicodechar{≤}{\ensuremath{\leq}}
+\newunicodechar{∈}{\ensuremath{\in}}
+\newunicodechar{∉}{\ensuremath{\not \in}}
+\newunicodechar{∖}{\ensuremath{\setminus}}
+\newunicodechar{◦}{\ensuremath{\circ}}
+\newunicodechar{°}{\ensuremath{^\circ}}
 \newunicodechar{…}{\ifmmode\mathellipsis\else\textellipsis\fi}
-\newunicodechar{·}{\ensuremath{·}}
-\newunicodechar{⋯}{\ensuremath{⋯}}
-\newunicodechar{∅}{\ensuremath{∅}}
-\newunicodechar{⇒}{\ensuremath{⇒}}
+\newunicodechar{·}{\ensuremath{\cdot}}
+\newunicodechar{⋯}{\ensuremath{\cdots}}
+\newunicodechar{∅}{\ensuremath{\emptyset}}
+\newunicodechar{⇒}{\ensuremath{\Rightarrow}}
 
-\newunicodechar{⁰}{\ensuremath{⁰}}
-\newunicodechar{¹}{\ensuremath{¹}}
-\newunicodechar{²}{\ensuremath{²}}
-\newunicodechar{³}{\ensuremath{³}}
-\newunicodechar{⁴}{\ensuremath{⁴}}
-\newunicodechar{⁵}{\ensuremath{⁵}}
-\newunicodechar{⁶}{\ensuremath{⁶}}
-\newunicodechar{⁷}{\ensuremath{⁷}}
-\newunicodechar{⁸}{\ensuremath{⁸}}
-\newunicodechar{⁹}{\ensuremath{⁹}}
-\newunicodechar{ⁱ}{\ensuremath{ⁱ}}
+\newunicodechar{⁰}{\ensuremath{^0}}
+\newunicodechar{¹}{\ensuremath{^1}}
+\newunicodechar{²}{\ensuremath{^2}}
+\newunicodechar{³}{\ensuremath{^3}}
+\newunicodechar{⁴}{\ensuremath{^4}}
+\newunicodechar{⁵}{\ensuremath{^5}}
+\newunicodechar{⁶}{\ensuremath{^6}}
+\newunicodechar{⁷}{\ensuremath{^7}}
+\newunicodechar{⁸}{\ensuremath{^8}}
+\newunicodechar{⁹}{\ensuremath{^9}}
+\newunicodechar{ⁱ}{\ensuremath{^i}}
+\newunicodechar{⁺}{\ensuremath{^+}}
 
-\newunicodechar{⌈}{\ensuremath{⌈}}
-\newunicodechar{⌉}{\ensuremath{⌉}}
-\newunicodechar{⌊}{\ensuremath{⌊}}
-\newunicodechar{⌋}{\ensuremath{⌋}}
+\newunicodechar{⌈}{\ensuremath{\lceil}}
+\newunicodechar{⌉}{\ensuremath{\rceil}}
+\newunicodechar{⌊}{\ensuremath{\lfloor}}
+\newunicodechar{⌋}{\ensuremath{\rfloor}}
 
-\newunicodechar{≅}{\ensuremath{≅}}
-\newunicodechar{⇔}{\ensuremath{⇔}}
-\newunicodechar{∃}{\ensuremath{∃}}
-\newunicodechar{±}{\ensuremath{±}}
+\newunicodechar{≅}{\ensuremath{\cong}}
+\newunicodechar{⇔}{\ensuremath{\Leftrightarrow}}
+\newunicodechar{∃}{\ensuremath{\exists}}
+\newunicodechar{±}{\ensuremath{\pm}}
 
 
 %
@@ -227,7 +229,7 @@
 \DeclareMathOperator{\red}{red}
 \DeclareMathOperator{\reg}{reg}
 \DeclareMathOperator{\sat}{sat}
-\DeclareMathOperator{\sEnd}{ℰ\negthinspace \mathit{nd}}
+\DeclareMathOperator{\sEnd}{\sE\negthinspace \mathit{nd}}
 \DeclareMathOperator{\sing}{sing}
 \DeclareMathOperator{\Spec}{Spec}
 \DeclareMathOperator{\Sym}{Sym}
@@ -237,30 +239,30 @@
 \DeclareMathOperator{\Frob}{Frob}
 
 % Sheaves
-\newcommand{𝒜}{\scr{A}}
-\newcommand{ℬ}{\scr{B}}
-\newcommand{𝒞}{\scr{C}}
-\newcommand{𝒟}{\scr{D}}
-\newcommand{ℰ}{\scr{E}}
-\newcommand{ℱ}{\scr{F}}
-\newcommand{𝒢}{\scr{G}}
-\newcommand{ℋ}{\scr{H}}
+\newcommand{\sA}{\scr{A}}
+\newcommand{\sB}{\scr{B}}
+\newcommand{\sC}{\scr{C}}
+\newcommand{\sD}{\scr{D}}
+\newcommand{\sE}{\scr{E}}
+\newcommand{\sF}{\scr{F}}
+\newcommand{\sG}{\scr{G}}
+\newcommand{\sH}{\scr{H}}
 \newcommand{\sHom}{\scr{H}\negthinspace om}
 \newcommand{\sI}{\scr{I}}
-\newcommand{𝒥}{\scr{J}}
+\newcommand{\sJ}{\scr{J}}
 \newcommand{\sK}{\scr{K}}
-\newcommand{ℒ}{\scr{L}}
-\newcommand{ℳ}{\scr{M}}
+\newcommand{\sL}{\scr{L}}
+\newcommand{\sM}{\scr{M}}
 \newcommand{\sN}{\scr{N}}
-\newcommand{𝒪}{\scr{O}}
+\newcommand{\sO}{\scr{O}}
 \newcommand{\sP}{\scr{P}}
-\newcommand{𝒬}{\scr{Q}}
+\newcommand{\sQ}{\scr{Q}}
 \newcommand{\sR}{\scr{R}}
-\newcommand{𝒮}{\scr{S}}
-\newcommand{𝒯}{\scr{T}}
+\newcommand{\sS}{\scr{S}}
+\newcommand{\sT}{\scr{T}}
 \newcommand{\sU}{\scr{U}}
 \newcommand{\sV}{\scr{V}}
-\newcommand{𝒲}{\scr{W}}
+\newcommand{\sW}{\scr{W}}
 \newcommand{\sX}{\scr{X}}
 \newcommand{\sY}{\scr{Y}}
 \newcommand{\sZ}{\scr{Z}}
@@ -275,32 +277,32 @@
 \newcommand{\cV}{\mathcal V}
 
 % Blackboard Bold Symbols
-\newcommand{𝔸}{\mathbb{A}}
-\newcommand{𝔹}{\mathbb{B}}
-\newcommand{ℂ}{\mathbb{C}}
-\newcommand{𝔻}{\mathbb{D}}
-\newcommand{𝔼}{\mathbb{E}}
-\newcommand{𝔽}{\mathbb{F}}
-\newcommand{𝔾}{\mathbb{G}}
+\newcommand{\bA}{\mathbb{A}}
+\newcommand{\bB}{\mathbb{B}}
+\newcommand{\bC}{\mathbb{C}}
+\newcommand{\bD}{\mathbb{D}}
+\newcommand{\bE}{\mathbb{E}}
+\newcommand{\bF}{\mathbb{F}}
+\newcommand{\bG}{\mathbb{G}}
 \newcommand{\bH}{\mathbb{H}}
 \newcommand{\bI}{\mathbb{I}}
 \newcommand{\bJ}{\mathbb{J}}
 \newcommand{\bK}{\mathbb{K}}
 \newcommand{\bL}{\mathbb{L}}
 \newcommand{\bM}{\mathbb{M}}
-\newcommand{ℕ}{\mathbb{N}}
+\newcommand{\bN}{\mathbb{N}}
 \newcommand{\bO}{\mathbb{O}}
-\newcommand{ℙ}{\mathbb{P}}
-\newcommand{ℚ}{\mathbb{Q}}
-\newcommand{ℝ}{\mathbb{R}}
+\newcommand{\bP}{\mathbb{P}}
+\newcommand{\bQ}{\mathbb{Q}}
+\newcommand{\bR}{\mathbb{R}}
 \newcommand{\bS}{\mathbb{S}}
 \newcommand{\bT}{\mathbb{T}}
 \newcommand{\bU}{\mathbb{U}}
 \newcommand{\bV}{\mathbb{V}}
 \newcommand{\bW}{\mathbb{W}}
-\newcommand{𝕏}{\mathbb{X}}
+\newcommand{\bX}{\mathbb{X}}
 \newcommand{\bY}{\mathbb{Y}}
-\newcommand{ℤ}{\mathbb{Z}}
+\newcommand{\bZ}{\mathbb{Z}}
 
 % Sans serif symbols
 \newcommand{\aB}{{\sf B}}
@@ -343,15 +345,15 @@
 \newtheorem{setting}[thm]{Setting}
 \newtheorem{warning}[thm]{Warning}
 
-% Numbering of equations.  Number equation subordniate to theorems.
+% Numbering of equations. Number equation subordniate to theorems.
 \numberwithin{equation}{thm}
 
-% Style for enumerated lists.  The following makes sure that enumerated lists are
+% Style for enumerated lists. The following makes sure that enumerated lists are
 % numbered in the same way as equations are.
 \setlist[enumerate]{label=(\thethm.\arabic*), before={\setcounter{enumi}{\value{equation}}}, after={\setcounter{equation}{\value{enumi}}}}
 
 % Shorthand notations
-\newcommand{↪}{↪}
+\newcommand{\into}{\hookrightarrow}
 \newcommand{\onto}{\twoheadrightarrow}
 \newcommand{\wtilde}{\widetilde}
 \newcommand{\what}{\widehat}
@@ -374,4 +376,4 @@
 \newcommand\CounterStep{\addtocounter{thm}{1}\setcounter{equation}{0}}
 
 % factor - quotient groups
-\newcommand{\factor}[2]{\left.  \raise 2pt\hbox{$#1$} \right/\hskip -2pt\raise -2pt\hbox{$#2$}}
+\newcommand{\factor}[2]{\left. \raise 2pt\hbox{$#1$} \right/\hskip -2pt\raise -2pt\hbox{$#2$}}