% Loading packages
\usepackage{ae}
\usepackage[T1]{fontenc}
\usepackage[english]{babel}
\usepackage{fontspec}
\usepackage{alphabeta}
\usepackage{bookmark}
\hypersetup{
	colorlinks=true,
	linkcolor=blue,
	filecolor=magenta,      
	urlcolor=cyan
}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{bbm}
\usepackage{stmaryrd}
\usepackage{csquotes}
\usepackage{listings}
\usepackage{lstautogobble}
\usepackage{svg}
\usepackage{tikz}
\usepackage{multirow}
\usepackage{multicol}
\usepackage{tcolorbox}
\usepackage{mdframed}
\usepackage{proof}
\usepackage{xparse}
\usepackage{cprotect}
\usepackage{titlesec}
\usepackage{xpatch}
\usepackage{enumitem}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{mathtools}
\usepackage[page,header]{appendix}
\usepackage{minitoc}
\usepackage{mathtools}
\usepackage{textgreek}
\usepackage{pdfpages}
\usepackage{lipsum}
\usepackage{newunicodechar}
\usepackage{txfonts}
\usepackage{yade}
\usepackage[backend=biber,style=numeric]{biblatex}
\usepackage{hyperref}

\usepackage[textheight=0.75\paperheight]{geometry}

\usepackage[lighttt]{lmodern}
\usetikzlibrary{shapes.geometric,positioning,backgrounds}

% Macros caractères globales
\newcommand{\pgrph}{\P}
\newcommand{\hsep}{\vspace{.2cm}\centerline{\rule{0.8\linewidth}{.05pt}}\vspace{.4cm}}
\renewcommand{\P}{\mathbb{P}}
\newcommand{\E}{\mathbb{E}}
\newcommand{\1}{\scalebox{1.2}{$\mathbbm{1}$}}
\newcommand{\floor}[1]{\left\lfloor#1\right\rfloor}
\newcommand{\littleO}{o}
\newcommand{\bigO}{\mathcal{O}}
\newcommand{\longdash}{\:\textrm{---}\:}
\newcommand\hole{\left[\raisebox{-0.25ex}{\scalebox{1.2}{$\cdot$}}\right]}
\newcommand\bracket[1]{\!\left[#1\right]}
\newcommand\spacebar{\;|\;}
\def\nDownarrow{\not\mspace{1mu}\Downarrow}
\let\pprec\preccurlyeq


% Création des environnement globaux
\newtheorem{theorem}{Theorem}
\newtheorem{definition}{Definition}
\newtheorem{property}{Property}
\newtheorem{remark}{Remark}

\newcounter{rule}

% Commandes logiques globales
\newcommand{\ifnullthenelse}[3]{
	\ifnum\value{#1}=0
	#2
	\else
	#3
	\fi
}

%%% Commande \newtag permettant de changer le label d'une equation
\makeatletter
\newcommand\newtag[2]{#1\def\@currentlabel{#1}\label{#2}}
\makeatother


% Macros caractères spécifiques au document
\newfontface\russian{Liberation Serif}
\newcommand\BB{{\ensuremath{\mathcal{B}}}}
\newcommand\en{{\text{\russian н}}}
\newcommand\TT{{\ensuremath{\mathcal{T}}}}
\newcommand\UU{{\ensuremath{\mathcal{U}}}}
\newcommand\CC{{\ensuremath{\mathcal{C}}}}
\newcommand\El{{\ensuremath{\operatorname{\mathcal{E}l}}}}
\newcommand\ii{{\ensuremath{\mathbf{i}}}}
\newcommand\Con{{\ensuremath{\operatorname{Con}}}}
\newcommand\Ty{{\ensuremath{\operatorname{Ty}}}}
\newcommand\Tm{{\ensuremath{\operatorname{Tm}}}}
\newcommand\Cstr{{\ensuremath{\operatorname{\mathcal{C}str}}}}
\newcommand\Rtsc{{\ensuremath{\operatorname{\mathcal{R}tsc}}}}
\newcommand\Cat{{\ensuremath{\operatorname{\mathcal{C}at}}}}
\newcommand\Set{{\ensuremath{\operatorname{\mathcal{S}et}}}}
\newcommand\FamSet{{\ensuremath{\operatorname{\mathcal{F}am\mathcal{S}et}}}}
\newcommand\Hom{{\ensuremath{\operatorname{\mathcal{H}om}}}}
\newcommand\this{{\ensuremath{\operatorname{\texttt{this}}}}}
\newcommand\one{{\ensuremath{\mathbf{1}}}}
\newcommand\dash{{\;\textrm{---}\;}}
\renewcommand\enquote[1]{``#1''}
\newcommand\tl{{\triangleleft}}

\DeclareMathOperator{\inj}{inj}
\DeclareMathOperator{\id}{id}
\DeclareMathOperator{\Id}{\mathcal{I}d}

\newcommand\TSet{{\ensuremath{\left[\TT,\Set\right]}}}
\newcommand\TSetObject[3]{{\ensuremath{
\left[
\begin{tikzpicture}[baseline=(base)]
	\node (U) at (0,0) {\UU};
	\node (El) at (0,1) {\El};
	\draw[->] (El) -- node[anchor=east] {\ensuremath{\scriptstyle p}} (U);
	
	\node (XU) at (1,0) {\ensuremath{#3}};
	\node (XEl) at (1,1) {\ensuremath{#1}};
	\draw[->] (XEl) -- node[anchor=west] {\ensuremath{\scriptstyle #2}} (XU);
	
	\draw[|->] (.3,0) -- (.7,0);
	\draw[|->] (.3,0.5) -- (.7,0.5);
	\draw[|->] (.3,1) -- (.7,1);
	
	\coordinate (base) at (.5,.4);
\end{tikzpicture}
\right]
}}}

\newcommand\simpleArrow[3]{
	\begin{tikzpicture} 
		\node (0) at (0,0) {$#1$}; 
		\node (1) at (6,0) {$#3$};
		\path[->] (0) edge["${\scriptstyle #2}$", pos=0.5, fore, black,=>, ] (1); 
	\end{tikzpicture}
}

\newcommand\diagram[1]{\begin{tcolorbox}\begin{center}\vspace{1.5cm}\Huge \texttt{\textbf{#1}}\vspace{1.5cm}\end{center}\end{tcolorbox}}

\newcommand\todo[1]{\begin{tcolorbox}[colback=red!20!white,colframe=red!85!black,boxrule=4pt] #1 \end{tcolorbox}}
\newcommand\inlinetodo[1]{\colorbox{orange}{#1}}
% Création des environnements spécifiques au document


%%% Subparaghaphs box
\newtcbox{\subparaghaphbox}{nobeforeafter,tcbox raise base, arc=9pt, outer arc=9pt, boxsep=2pt,left=2pt,right=2pt,top=2pt,bottom=2pt,boxrule=1pt,colback=white!85!orange}
\newcommand{\subparaghaphboxedcontent}[1]{\subparaghaphbox{#1}\newline}
%\titleclass{\mathcases}{straight}[\subparagraph]
\titleformat{\subparagraph}[runin]{\normalfont\normalsize\bfseries}{}{0em}{\subparaghaphboxedcontent}
\titlespacing*{\subparagraph}{0pt}{3.25ex plus 1ex minus .2ex}{0.5em}

\addbibresource{Bilibibio.bib}