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%!TEX root = index_theory.tex
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% -- Author: Jannes Bantje, j.bantje@wwu.de
\documentclass[%
    a4paper,
    index=totoc,
    toc=bibliography,
	listof=totoc,
    fontsize=10,
    DIV=13,
    headinclude,
    twoside,
    BCOR=12mm,
    cleardoublepage=empty,
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    draft
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]{scrbook}

\usepackage{etoolbox}
\usepackage{xstring}


%--Farbdefinitionen und Grafiken (muss vor tikz geladen werden)
% ======================================================================================
\usepackage[usenames, table, x11names]{xcolor}
\definecolor{dark_gray}{gray}{0.45}
\definecolor{light_gray}{gray}{0.6}
\definecolor{fb10_blue}{cmyk}{0.8,0.4,0.13,0.07}
\colorlet{maincolour}{fb10_blue}
\usepackage[final]{graphicx}
% ======================================================================================


%--Zum Zeichnen/ TikZ-Kram (vor polyglossia bzw. babel geladen werden)
% ======================================================================================
\usepackage{tikz}
\usepackage{tikz-cd}
\usepackage{tikzpagenodes}
\usetikzlibrary{%
	arrows.meta,
	positioning,
	calc
}
\tikzset{>=Stealth}
\tikzset{% to circumvent incompatibility with " being an active character
  every picture/.append style={
    execute at begin picture={\shorthandoff{"}},% chktex 18
    execute at end picture={\shorthandon{"}}% chktex 18
  }
}
% ======================================================================================

%-- Mathepakete etc.
% ======================================================================================
\usepackage[T1]{fontenc}
\renewcommand{\rmdefault}{zpltlf}
\usepackage{mathtools} % beinhaltet amsmath
\mathtoolsset{centercolon,showmanualtags}
\newtagform{brackets}{[}{]}% chktex 9
\usetagform{brackets}
\makeatletter
\long\def\theequation{\@fnsymbol \c@equation}
\makeatother
\usepackage{fix-cm}
\usepackage[bbgreekl]{mathbbol}
\usepackage{amssymb,marvosym}
\usepackage{xfrac}
\usepackage{mathdots} % Verbesserung von Punkten wie zB \ldots
\usepackage{centernot}
\usepackage{stackrel}
\usepackage{nicematrix}
\DeclareSymbolFont{bbold}{U}{bbold}{m}{n}
% \DeclareFontShape{U}{bbold}{m}{n}{%
%    <-9> gen * bbold
%    <10-10.95> bbold10
%    <12-14.4> bbold12
%    <17.28-> bbold17
% }{}
\usepackage{anyfontsize}
\DeclareSymbolFontAlphabet{\mathbbold}{bbold}
\newcommand{\ind}{\mathbbold{1}} % charakteristische-Funktion-Eins
\renewcommand{\le}{\leqslant}
\renewcommand{\ge}{\geqslant}
% ======================================================================================

\input{math.tex}

%-- Typographie/Polyglossia
% ======================================================================================
\usepackage[euler-digits]{eulervm} % vor fontspec laden!
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\usepackage[bb=px,scr=boondoxo]{mathalpha} % \mathbb als px font
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\DeclareFontFamily{U}{rsfs}{\skewchar\font127 }
\DeclareFontShape{U}{rsfs}{m}{n}{%
   <-6> rsfs5
   <6-8> rsfs7
   <8-> rsfs10
}{}
\usepackage[no-math]{fontspec}
\usepackage{polyglossia} % moderner babel-ersatz
\setmainlanguage[variant=british]{english}
\setotherlanguages{german,russian}

\defaultfontfeatures{Mapping=tex-text,WordSpace={1.3},Ligatures={Required,Common,Contextual},Extension=.otf}%
% \usepackage[usefilenames,%
% 	RM={Scale=0.94},
% 	RMstyle={Semibold},
% 	SS={Scale=0.94},
% 	TT={Scale=MatchLowercase,FakeStretch=0.9},
% 	RMSCfont=texgyretermes,
% 	SSSCfont=texgyreheros]{plex-otf}

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% \setmainfont{IBMPlexSerif}[Scale=.93,UprightFont=*-Regular,BoldFont=*-SemiBold,ItalicFont=*-Italic,BoldItalicFont=*-MediumItalic,UprightFeatures={SmallCapsFont=XCharter-Roman},ItalicFeatures={SmallCapsFont=XCharter-Italic},SmallCapsFeatures={Letters=SmallCaps,Scale=1},Numbers=OldStyle,StylisticSet={4}]
% \setsansfont{IBMPlexSans}[Scale=.96,UprightFont=*-Regular,BoldFont=*-Bold,ItalicFont=*-Italic,BoldItalicFont=*-BoldItalic,StylisticSet={3}]
% \setmonofont{IBMPlexMono}[Scale=MatchLowercase,UprightFont=*-Regular,BoldFont=*-Bold,ItalicFont=*-Italic,BoldItalicFont=*-BoldItalic]
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% \setmainfont{TeXGyrePagellaX}[UprightFont=*-Regular,BoldFont=*-Bold,ItalicFont=*-Italic,BoldItalicFont=*-BoldItalic,ItalicFeatures={Style=Historic},Ligatures={Required,Common,Contextual,Historic}]
% \setmainfont{XCharter}[UprightFont=*-Roman,BoldFont=*-Bold,ItalicFont=*-Italic,BoldItalicFont=*-BoldItalic,ItalicFeatures={Style=Historic},Ligatures={Required,Common,Contextual,Historic}]
% \setmainfont{Coelacanth}[Scale=1.1,UprightFont=*,BoldFont=*Bold,ItalicFont=*Italic,BoldItalicFont=*Italic,ItalicFeatures={Style=Historic},Ligatures={Required,Common,Contextual,Historic}]
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\setmainfont{SourceSerifPro}[UprightFont=*-Regular,BoldFont=*-Bold,ItalicFont=*-RegularIt,BoldItalicFont=*-BoldIt,ItalicFeatures={Style=Historic},Ligatures={Required,Common,Contextual,Historic}]
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% \setsansfont{texgyreadventor}[Scale=MatchUppercase, UprightFont=*-regular, BoldFont=*-bold, ItalicFont=*-italic, BoldItalicFont=*-bolditalic]

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\setsansfont{SourceSansPro}[Scale=MatchUppercase,UprightFont=*-Regular, BoldFont=*-Bold, ItalicFont=*-RegularIt, BoldItalicFont=*-BoldIt]
\setmonofont{SourceCodePro}[Scale=0.9,UprightFont=*-Regular, BoldFont=*-Semibold, ItalicFont=*-Light]
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\newfontfamily\cyrillicfont{XCharter}

\usepackage{fontawesome}
\usepackage{academicons}
\usepackage[final]{microtype}
\usepackage[draft=false]{scrlayer-scrpage}
\AtBeginDocument{\setlength\parindent{1.4em}}
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\linespread{1.1}
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\flushbottom

\usepackage{lettrine}
\setcounter{DefaultLines}{2}
\setlength{\DefaultFindent}{.4pt}
\setlength{\DefaultNindent}{0em}
\renewcommand*{\DefaultLoversize}{0.1}
% ======================================================================================

%-- Lists
% ======================================================================================
\addtokomafont{descriptionlabel}{\normalfont\bfseries}
\addtokomafont{labelinglabel}{\normalfont\bfseries}
\usepackage[shortlabels]{enumitem}
% \setlist[itemize,1]{label=\faCaretRight}
\setlist{itemsep=0pt}
\setlist[itemize,1]{label=\textcolor{black}{\raisebox{.4ex}{\rule{.65ex}{.65ex}}}}
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\setlist[enumerate]{font=\normalfont\bfseries}
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\setlist[description]{font=\normalfont\bfseries}


\newlist{steps}{enumerate}{1}
\setlist[steps]{label=Step\ \arabic*,align=left,font=\normalfont\bfseries,labelsep=1ex,topsep=0mm,labelwidth=*,leftmargin=\parindent, after=\vspace{2mm plus 1mm minus 1mm}}
% [label=Step\ \arabic*,leftmargin=*,labelwidth=*,topsep=0mm,align=left]
\usepackage{multicol}
% ======================================================================================


%-- Floats and Tables
% ======================================================================================
\usepackage{booktabs}
\usepackage{wrapfig}
\addtokomafont{captionlabel}{\sffamily\bfseries}
\usepackage[caption=false]{subfig}
\captionsetup[subfigure]{subrefformat=simple,labelformat=simple,listofformat=subsimple,captionskip=1.5em}
\renewcommand\thesubfigure{(\alph{subfigure})}
\makeatletter
\renewcommand*{\@pnumwidth}{2em}% Width of the page number column in the table of contents.
\makeatother
% ======================================================================================


%-- korrekte Anführungszeichen und Zitierbefehle
% ======================================================================================
\usepackage[autostyle,german=quotes,english=british]{csquotes}
% ======================================================================================

%--index stuff
% ======================================================================================
\usepackage{makeidx}
\newcommand{\bet}[1]{\textcolor{maincolour}{\emph{\bfseries#1}}}
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% \newcommand{\Index}[1]{\bet{#1}\index{#1}}
\NewDocumentCommand{\Index}{ O{#2} m }{\bet{#2}\index{#1}}
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\makeindex
\renewcommand{\indexpagestyle}{scrheadings}
% ======================================================================================

%-- Todonotes, Footnotes, Marginnotes
% ======================================================================================
\deffootnote[1.5em]{1.5em}{1.5em}{\textsuperscript{\thefootnotemark}\ }
\usepackage[fulladjust]{marginnote}
\renewcommand*{\marginfont}{\itshape\footnotesize}
\usepackage{ragged2e}
\renewcommand*{\raggedleftmarginnote}{\RaggedLeft}
\renewcommand*{\raggedrightmarginnote}{\RaggedRight}
\usepackage[textsize=small,obeyFinal,colorinlistoftodos]{todonotes}
\newcommand{\todoAsk}[1]{\todo[color=Chartreuse3!60]{#1}}
\newcommand{\todoCake}[1]{\todo[color=DodgerBlue3!60]{#1}} % for "icing on the cake"
\newcommand{\todoInCake}[1]{\todo[color=DodgerBlue3!60,inline,noinlinepar,inlinewidth=3cm]{#1}} % for "icing on the cake"
% \newcommand{\pqfix}{\todo[color=DarkOrchid2!60]{fix $(p,q)$}}
% \newcommand{\pqfixIn}{\todo[color=DarkOrchid2!60,inline,noinlinepar,inlinewidth=2cm]{fix $(p,q)$}}
% ======================================================================================

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\KOMAoptions{DIV=last}

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% -- BibLaTeX
% ======================================================================================
\PassOptionsToPackage{hyphens}{url}
\usepackage[%
	backend=biber,
	sortlocale=auto,
	hyperref,
	backref,
	style=alphabetic,
	autolang=langname,
	sorting=nyt
	]%
{biblatex}
\DeclareLanguageMapping{english}{british}
\renewcommand*{\mkbibnamefamily}[1]{%
  \ifmknamesc{\textsc{#1}}{#1}}
\renewcommand*{\mkbibnameprefix}[1]{%
  \ifboolexpr{ test {\ifmknamesc} and test {\ifuseprefix} }
    {\textsc{#1}}
    {#1}}
\def\ifmknamesc{%
  \ifboolexpr{ test {\ifcurrentname{labelname}}
               or test {\ifcurrentname{author}}
               or ( test {\ifnameundef{author}} and test {\ifcurrentname{editor}} ) }}%
% \addbibresource{literature.bib}
% ======================================================================================


%--Konfiguration von Hyperref und Cleveref
% ======================================================================================
% \usepackage{thmtools}
\usepackage[%
	final,
	pdfencoding=auto, % for lualatex
	bookmarksopen=true, % bookmarktree expaned in Adobe Acrobat
	bookmarksnumbered=true, % include section numbers if requested
	pdfpagelabels, % set pdf page labels
	pagebackref, % include links in bibliography
	backref=false, 
	hidelinks, % remove colour and border
	linkcolor=black,
	citecolor=black,
	pdfborderstyle={/S/U},
	linkbordercolor=SkyBlue2,
	urlcolor=SkyBlue2, 
	pdfauthor={Jannes Bantje},
]{hyperref}
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\usepackage[nameinlink,noabbrev,capitalise]{cleveref}
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\newcommand{\appendLink}[1]{#1\,\faExternalLink}
\newcommand{\hrefsym}[2]{\href{#1}{\texttt{\appendLink{#2}}}}
\newcommand{\hrefsymX}[2]{\href{#1}{\appendLink{#2}}}
\newcommand{\hrefsymmail}[2]{\href{#1}{\texttt{\faEnvelopeO\,#2}}}
\renewcommand{\url}[1]{\hrefsym{#1}{\nolinkurl{#1}}}
% ======================================================================================

% -- theorem packages
% ======================================================================================
\usepackage{amsthm}
\usepackage{bookmark}
% \bookmarksetup{open,numbered}

% \declaretheoremstyle[%
% 	headfont=\itshape\scshape,
% 	bodyfont=\normalfont,
% 	headpunct=.,
% 	postheadspace=1em,
% 	spacebelow=12pt,spaceabove=2pt,
% 	qed=\qedsymbol]%
% {proofs}
% \let\proof\relax
% \declaretheorem[name=Proof,numbered=no,style=proofs]{proof}

\colorlet{tcb-bg-color}{black!5!white}

\usepackage{tcolorbox}
\tcbuselibrary{skins,xparse,breakable}
\tcbset{%
	basestyle/.style={enhanced,
		attach title to upper={\ \setlength\parindent{1.4em}},
		fontupper=\normalfont,fonttitle=\sffamily\bfseries\upshape,
		frame empty,boxrule=0mm,arc=0mm,
		left = 2.3mm,top=.7mm,bottom=.7mm,right=0.7mm,boxsep=0.5mm,
		borderline west={0.5mm}{0mm}{maincolour},
		borderline west={0.5mm}{.90mm}{maincolour},
		% borderline west={0.5mm}{1.80mm}{maincolour},
		drop small lifted shadow,
		after skip=3mm plus 1mm minus 1mm,
		bookmark=\protect\tcbtitletext,
		% segmentation style={black},
		sidebyside align=center seam,
		sidebyside gap=7mm,
		% IfNoValueTF{\tcbtitletext}{bookmark={Generic Bookmark}}{bookmark={\tcbtitletext}},
		},
	defstyle/.style={basestyle,coltitle=maincolour,colback=tcb-bg-color},
    theostyle/.style={basestyle,coltitle=maincolour,colback=tcb-bg-color},
	blankstyle/.style={basestyle,empty,coltitle=black,breakable,no shadow,no borderline,size=minimal,before skip=4mm plus 1mm minus 1mm}
}
\DeclareTColorBox[auto counter,number within=section,crefname={Definition}{Definitions}]{definition}{ g O{} t\label g }{%
	defstyle,IfValueTF={#1}{title={Definition~\thetcbcounter\ --\ #1}}{title=Definition~\thetcbcounter}, IfBooleanTF={#3}{label=#4}{},#2
	}
\DeclareTColorBox[use counter from=definition,crefname={Proposition}{Propositions}]{proposition}{ g O{} t\label g }{%
	theostyle,IfValueTF={#1}{title={Proposition~\thetcbcounter\ ---\ #1}}{title=Proposition~\thetcbcounter}, IfBooleanTF={#3}{label=#4}{},#2
	}
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\DeclareTColorBox[use counter from=definition,crefname={Proposition \& Definition}{Propositions}]{propositiondef}{ g O{} t\label g }{%
	theostyle,IfValueTF={#1}{title={Proposition~\thetcbcounter\ ---\ #1}}{title=Proposition \& Definition~\thetcbcounter}, IfBooleanTF={#3}{label=#4}{},#2
	}
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\DeclareTColorBox[use counter from=definition,crefname={Lemma}{Lemmas}]{lemma}{ g O{} t\label g }{%
	theostyle,IfValueTF={#1}{title={Lemma~\thetcbcounter\ --\ #1}}{title=Lemma~\thetcbcounter}, IfBooleanTF={#3}{label=#4}{},#2
	}
\DeclareTColorBox[use counter from=definition,crefname={Corollary}{Corollaries}]{corollary}{ g O{} t\label g }{%
	theostyle,IfValueTF={#1}{title={Corollary~\thetcbcounter\ --\ #1}}{title=Corollary~\thetcbcounter}, IfBooleanTF={#3}{label=#4}{},#2
	}
\DeclareTColorBox[use counter from=definition,crefname={Theorem}{Theorems}]{theorem}{ g O{} t\label g }{%
	theostyle,IfValueTF={#1}{title={Theorem~\thetcbcounter\ ---\ #1}}{title=Theorem~\thetcbcounter}, IfBooleanTF={#3}{label=#4}{},#2
	}
\DeclareTColorBox[use counter from=definition,crefname={Example}{Examples}]{example}{ g O{} t\label g }{%
	blankstyle,IfValueTF={#1}{title={Example~\thetcbcounter\ --\ #1}}{title=Example~\thetcbcounter}, IfBooleanTF={#3}{label=#4}{},#2
	}
\DeclareTColorBox[use counter from=definition,crefname={Remark}{Remarks}]{remark}{ g O{} t\label g }{%
	blankstyle,IfValueTF={#1}{title={Remark~\thetcbcounter\ --\ #1}}{title=Remark~\thetcbcounter}, IfBooleanTF={#3}{label=#4}{},#2
	}
\DeclareTColorBox[use counter from=definition,crefname={Notation}{Notations}]{notation}{ g O{} t\label g }{%
	blankstyle,IfValueTF={#1}{title={Notation~\thetcbcounter\ --\ #1}}{title=Notation~\thetcbcounter}, IfBooleanTF={#3}{label=#4}{},#2
	}
% ======================================================================================

%-- nice email adress command (after http://tex.stackexchange.com/a/663/67086)
%----------------------------------------------------------------------------------------
\catcode`\_=11\relax
\newcommand\email[1]{\_email #1\q_nil}
\def\_email#1@#2\q_nil{%
  \href{mailto:#1@#2}{{\emailfont #1\emailampersat #2}}
}
\newcommand\emailfont{\ttfamily}
\newcommand\emailampersat{{\fontsize{10.9pt}{12pt}\selectfont\sffamily@}}
\catcode`\_=8\relax
%----------------------------------------------------------------------------------------