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2 % Things dealing with arrows in a category. Or functions, basically.
4 \ifx\havemjoarrow\undefined
10 % The identity operator/arrow on its argument.
11 \newcommand*
{\identity}[1]{ \operatorname{id
}_
{{#1}} }
13 % The composition of two arrows/functions. For example, the
14 % composition of g with f is \compose{g}{f}\of{x} === g\of{f\of{x}}.
15 \newcommand*
{\compose}[2]{ {#1}\circ{#2} }
17 % The inverse of an arrow, function, or whatever.
18 \newcommand*
{\inverse}[1]{ #1^
{-
1} }
20 % The preimage of the second argument (a set) under the first (a function).
21 \newcommand*
{\preimage}[2]{ #1^
{-
1}\of{#2} }