\newcommand{\Con}{\mathrm{Con}}
\newcommand{\conf}[1]{\mathscr{C}(#1)}
\newcommand{\cov}{{{\mathrel-\joinrel\subset}}}
\newcommand{\longcov}[1]{{\stackrel{#1}{\mathrel-\joinrel\relbar\joinrel\subset\,}}}
\newcommand{\ttrue}{\texttt{tt}}
\newcommand{\imc}{\rightarrowtriangle}
\newcommand{\ffalse}{\texttt{ff}}
\DeclareMathOperator{\pol}{pol}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{prop}[theorem]{Proposition}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{example}[theorem]{Example}
\newtheorem{exercise}[theorem]{Exercise}
\newtheorem{convention}[theorem]{Convention}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{remark}[theorem]{Remark}

%New arrow heads
\newdir{C}{%
!/4.5pt/@{( }*:(1,-.2)@{}*:(1,+.2)@_{}}

\newdir{|>}{%
!/4.5pt/@{|}*:(1,-.2)@{>}*:(1,+.2)@_{>}}

\renewcommand{\tilde}[1]{\widetilde{#1}}

\newcommand{\minconflict}[2]{\xymatrix { #1 \ar@{~}[r]& #2}}
\newdir{pb}{:(1,-1)@^{|-}}
\def\pb#1{\save[]+<16 pt,0 pt>:a(#1)\ar@{pb{}}[]\restore}

% Copycat
\newcommand{\CC}{{\rm C\!\!\!C}}
\newcommand{\cc}{\mathrm{\,c\!\!\!\!c\,}}

% Definitions for todonotes
\newcommand{\rkPierreInline}[1]{\todo[inline,color=blue!40]{Pierre --- #1}}
\newcommand{\rkPierre}[1]{\todo[color=blue!40]{Pierre --- #1}}
\newcommand{\rkSimonInline}[1]{\todo[inline,color=red!40]{Simon --- #1}}
\newcommand{\rkSimon}[1]{\todo[color=red!40]{Simon --- #1}}

% Pierre's macros
\newcommand{\coin}{\mathbf{coin}}
\newcommand{\coffee}{\mathbf{coffee}}
\newcommand{\tea}{\mathbf{tea}}
\newcommand{\tensor}{\otimes}
\newcommand{\ES}{\mathcal{E}}
\newcommand{\ESP}{\mathcal{EP}}
\newcommand{\proj}{\downarrow}
\newcommand{\secbij}[1]{\mathscr{B}^\text{sec}_{#1}}
\newcommand{\B}{{\mathbb B}}
\def\profto{\!\!\!\xymatrix@C-.75pc{\ar[r]|-{\! +\!} &}\!\!\! }%profarrow
\newcommand{\CG}{\mathrm{CG}}
\newcommand{\gr}{\mathrm{gr}}
\newcommand{\iso}{\cong}
\newcommand{\pto}{\rightharpoonup}
\newcommand{\hid}{\mathfrak{h}}
\newcommand{\inter}{\circledast}
\newcommand{\wit}{\mathrm{wit}}
\newcommand{\lift}[1]{\overline{#1}}
\newcommand{\op}{\mathrm{op}}
\newcommand{\conflict}{\mathrel{\sharp}}
\newcommand{\nconflict}{\mathrel{\not \sharp}}
