\documentclass{article} \usepackage[utf8]{inputenc} \usepackage{amsfonts, amsthm, amssymb, mathtools,etoolbox, amsmath} \usepackage{blindtext} \usepackage{hyperref} \usepackage{tikz,tikz-cd} \usepackage{array} \usepackage{xcolor} \usepackage{graphicx} \usepackage{framed} \usepackage{autobreak} \graphicspath{ {images/} } \usepackage[style=alphabetic,sorting=nyt]{biblatex} \renewbibmacro{in:}{} \addbibresource{bibl.bib} \tikzset{pullback/.style={minimum size=1.2ex,path picture={ \draw[opacity=1,black,-,#1] (-0.5ex,-0.5ex) -- (0.5ex,-0.5ex) -- (0.5ex,0.5ex);% }}} \theoremstyle{plain} \newtheorem{theorem}{Theorem}[section] \newtheorem{proposition}[theorem]{Proposition} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{conjecture}[theorem]{Conjecture} \theoremstyle{definition} \newtheorem{example}[theorem]{Example} \newtheorem{definition}[theorem]{Definition} \newtheorem{remark}[theorem]{Remark} \newtheorem{question}[theorem]{Question} \newtheorem{problem}[theorem]{Problem} \newtheorem*{answer}{Answer} \newcommand{\dq}[1]{``#1"} \newcommand{\memo}[1]{\textcolor{red}{memo: #1}} \newcommand{\N}{\mathbb{N}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\R}{\mathbb{R}} \newcommand{\Po}[1]{\mathcal{P}(#1)} \newcommand{\co}{\mathrm{c}} \newcommand{\Set}{\mathrm{Set}} \newcommand{\FinSet}{\mathrm{FinSet}} \newcommand{\Top}{\mathrm{Top}} \newcommand{\HeyAlg}{\mathrm{HeyAlg}} \newcommand{\Rieg}{\mathrm{Rieg}} \newcommand{\Ring}{\mathrm{Ring}} \newcommand{\ti}{\times} \newcommand{\ex}{\uparrow} \newcommand{\2}{\mathbf{2}} \newcommand{\mult}[1]{\mathrm{mult}(#1)} \newcommand{\mN}{\mult{\N}} \newcommand{\di}{\mathrm{dim}} \newcommand{\rad}{\mathrm{rad}} \newcommand{\Mr}[2]{\N_{#1,#2}} \newcommand{\End}{\mathrm{End}} \newcommand{\Groupoid}{\mathrm{Groupoid}} \newcommand{\Groupoidfin}{\Groupoid_{\mathrm{fin}}} \newcommand{\TB}{\star} \newcommand{\C}{\mathcal{C}} \newcommand{\ep}{\varepsilon} \newcommand{\loga}{log-able} \newcommand{\ch}{\mathrm{char}} \newcommand{\TV}{\Omega} \newcommand{\chz}{(\infty, 0)} \newcommand{\Tame}{\mathbb{T}\mathrm{ame}} \newcommand{\qTame}{\overline{\N\times \N_{>}}} \newcommand{\K}[1]{#1 / \hspace{-1pt} \scalebox{0.7}{$\cong$}} \newcommand{\biK}[1]{#1 / \hspace{-1pt} \scalebox{0.7}{$\simeq$}} \newcommand{\lcm}{\mathrm{lcm}} \newcommand\binuparrow{\mathbin{\uparrow}} \newcommand{\powow}{\binuparrow \binuparrow}