\usepackage{palatino}
\usepackage{euler}
\usepackage{amsthm}
\usepackage{amssymb}

\swapnumbers % 2.1 Theorem, instead of Theorem 2.1
% number these things within the section
\newtheorem{thm}{Theorem}[section]
\newtheorem*{thm*}{Theorem}
\newtheorem{lem}{Lemma}[section]
\newtheorem*{lem*}{Lemma}
\newtheorem{prop}{Proposition}
\newtheorem{cor}{Corollary}
\theoremstyle{definition}
\newtheorem{defn}{Definition}[section]
\newtheorem{exercise}{Exercise}[section]
\newtheorem*{exercise*}{Exercise}
\newtheorem{EG}{Example}[section]

\newcommand{\half}{{\textstyle \frac{1}{2}}}
\newcommand{\nin}{\not\in}
\newcommand{\set}[1]{\left\{#1\right\}}
\newcommand{\seq}[1]{\left<#1\right>}
\newcommand{\abs}[1]{\left|#1\right|}
\newcommand{\norm}[1]{\left\|#1\right\|}
\newcommand{\closure}[1]{\overline{#1}}
% \span already has a meaning
% FIXME: what's the notation for span?
\newcommand{\Span}[1]{{\mathrm span}\left<#1\right>}

\DeclareMathOperator{\coker}{coker}
\DeclareMathOperator{\image}{im}
\DeclareMathOperator{\im}{im}
\DeclareMathOperator{\rad}{rad}
\DeclareMathOperator{\Id}{Id}
\DeclareMathOperator{\grad}{grad}
\DeclareMathOperator{\Stab}{Stab}
\DeclareMathOperator{\Fix}{Fix}
\newcommand{\op}{{\mathrm op}} % opposite, as in opposite group/opposite category
\DeclareMathOperator{\Pow}{Pow} % Power set

\newcommand{\nequiv}{\not\equiv}
\newcommand{\he}{\simeq} % homotopy equivalent
\newcommand{\degrees}{^\circ}

\newcommand{\wreath}{\lmoustache} % wreath product
\newcommand{\semidirect}{\rtimes} % semidirect product

\newcommand{\restrict}{\vert}
\newcommand{\psmallmatrix}[1]{\left(\begin{smallmatrix}#1\end{smallmatrix}\right)}

\DeclareMathOperator{\Mod}{Mod}
\DeclareMathOperator{\Imm}{Imm}
\DeclareMathOperator{\Emb}{Emb}
\DeclareMathOperator{\Mono}{Mono}
\DeclareMathOperator{\Iso}{Iso}
\DeclareMathOperator{\Homeo}{Homeo}
\DeclareMathOperator{\Diff}{Diff}
\DeclareMathOperator{\Hom}{Hom}
\DeclareMathOperator{\Tor}{Tor}
\DeclareMathOperator{\Ext}{Ext}
\DeclareMathOperator{\Mat}{Mat} % Matrices
\DeclareMathOperator{\Alt}{Alt}
\DeclareMathOperator{\Arf}{Arf}
\DeclareMathOperator{\Sym}{Sym}
\DeclareMathOperator{\Out}{Out}
\DeclareMathOperator{\Inn}{Inn}
\DeclareMathOperator{\Aut}{Aut}
\DeclareMathOperator{\End}{End}
\DeclareMathOperator{\she}{she} % Self-(homotopy equivalences); this notation is awful
\DeclareMathOperator{\Wh}{Wh}
\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\SL}{SL}
\DeclareMathOperator{\Sp}{Sp}
\DeclareMathOperator{\OO}{O}
\DeclareMathOperator{\UU}{U}
\DeclareMathOperator{\SO}{SO}
\DeclareMathOperator{\Gr}{Gr} % grassmannian
%\DeclareMathOperator{\PGL}{PGL}
\DeclareMathOperator*{\holim}{holim}
\newcommand{\from}{\colon}
\newcommand{\ot}{\leftarrow} % can't use \from
\newcommand{\st}{\mid} % such that
\newcommand{\inj}{\hookrightarrow}
\newcommand{\surj}{\twoheadrightarrow}
%\newcommand{\isoto}{\overset{\sim}{\to}}
\newcommand{\isotoo}{\xrightarrow{\sim}}
\newcommand{\immto}{\looparrowright}
\newcommand{\dd}{\mathrm{d}}
\newcommand{\dt}{\,\mathrm{d}t}
\newcommand{\dx}{\,\mathrm{d}x}
\newcommand{\dy}{\,\mathrm{d}y}

\newcommand{\bA}{{\mathbf A}}
\newcommand{\bC}{{\mathbf C}}
\newcommand{\bF}{{\mathbf F}}
\newcommand{\bH}{{\mathbf H}}
\newcommand{\bL}{{\mathbf L}}
\newcommand{\bN}{{\mathbf N}}
\newcommand{\bO}{{\mathbf O}}
\newcommand{\bP}{{\mathbf P}}
\newcommand{\bQ}{{\mathbf Q}}
\newcommand{\bR}{{\mathbf R}}
\newcommand{\bS}{{\mathbf S}}
\newcommand{\bZ}{{\mathbf Z}}
\newcommand{\cB}{{\mathcal B}}
\newcommand{\cC}{{\mathcal C}}
\newcommand{\cD}{{\mathcal D}}
\newcommand{\cF}{{\mathcal F}}
\newcommand{\cG}{{\mathcal G}}
\newcommand{\cN}{{\mathcal N}}
\newcommand{\cO}{{\mathcal O}}
\newcommand{\cP}{{\mathcal P}}
\newcommand{\cR}{{\mathcal R}}
\newcommand{\cS}{{\mathcal S}}
\newcommand{\cT}{{\mathcal T}}

\newcommand{\RP}{{\mathbf {RP}}}
\newcommand{\CP}{{\mathbf {CP}}}
\newcommand{\HP}{{\mathbf {HP}}}
\newcommand{\OP}{{\mathbf {OP}}}

\newcommand{\review}[1]{\textbf{Review:} #1}
\newcommand{\Def}[1]{\emph{#1}}
\newcommand{\fixme}[1]{\textbf{FIXME: #1}}
\newcommand{\hint}[1]{\emph{hint:} #1}

\newcommand{\NB}[1]{\textbf{NB:} #1}
% \newcommand{\MNEU}[1]{\textbf{Mneumonic:} #1}
\newtheorem*{mneu}{Mneumonic}

% Cute pullquote environment
\newenvironment{pullquote}{\Large \begin{center}
``}{''\end{center}}
