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arrow category

\documentclass{article}
% this is the default PlanetMath preamble.  as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.

% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
%\usepackage{amscd}

% used for TeXing text within eps files
%\usepackage{psfrag}
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%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%%\usepackage{xypic}

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% define commands here

\begin{document}
Let $\mathcal{C}$ be a category.  The \emph{arrow category} of $\mathcal{C}$ is the functor category $\mathcal{C}^\textbf{2}$.  Here, $\textbf{2}$ is the ordinal category consisting of $0,1$.  Specifically, the contents of $\mathcal{C}^\textbf{2}$ are:
\begin{enumerate}
\item an object of $\mathcal{C}^\textbf{2}$ is an arrow (morphism) of $\mathcal{C}$
\item given two objects of $\mathcal{C}^\textbf{2}$, say $A \stackrel{f}{\longrightarrow} B$ and $A' \stackrel{g}{\longrightarrow} B'$, a morphism (of $\mathcal{C}^\textbf{2}$) from $f$ to $g$ consists of an ordered pair $(h,k)$, where $A \stackrel{h}{\longrightarrow} A'$ and $B \stackrel{k}{\longrightarrow} B'$, such that the following diagram
$$\xymatrix{
 A \ar[r]^h \ar[d]_{f} & A' \ar[d]^g \\ 
 B \ar[r]_k & B'}
$$
is a commutative diagram.
\end{enumerate}
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nd{document}