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prelude.tex
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\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
% IWCS
% included below \usepackage{graphicx} %%% for including graphics
% included below \usepackage{url} %%% for including URLs
\usepackage{times}
% included below: \usepackage{natbib}
\usepackage[margin=25mm]{geometry}
\usepackage{amsmath}
\usepackage{cases}
\usepackage{amsthm}
\usepackage{amsfonts}
\usepackage{mathtools}
\usepackage{natbib}
\usepackage{tikz}
\usepackage{pgf}
\usepackage{graphicx}
\usepackage{fullpage}
%\usepackage{caption}
\usepackage{subcaption}
\usepackage[caption=false]{subfig}
\usepackage{multicol}
\usepackage{todonotes}
\usepackage{float}
\usepackage{url}
\usetikzlibrary{arrows,automata}
\usetikzlibrary{positioning,calc,decorations.pathmorphing,decorations.pathreplacing,patterns}
\newtheorem{defi}{Definition}
\newtheorem{lemma}{Lemma}
\newtheorem{prop}{Proposition}
\newtheorem{thm}{Theorem}
\newtheorem{coro}{Corollary}
\usepackage{todonotes}
\renewcommand{\vec}[1]{%
\overrightarrow{#1}}
\renewcommand{\bar}[1]{%
\overline{#1}}
\newcommand{\cC}[0]{%
\mathcal{C}}
\newcommand{\ra}[0]{%
\rightarrow}
\DeclareMathOperator{\Ob}{Ob}
\DeclareMathOperator{\Vect}{Vect}
\DeclareMathOperator{\Aff}{Aff}
\DeclareMathOperator{\Mon}{Mon}
\DeclareMathOperator{\Nom}{Nom}
\DeclareMathOperator{\Cat}{Cat}
\DeclareMathOperator{\Net}{Net}