mjo-arrow.tex

   1 %
   2 % Things dealing with arrows in a category. Or functions, basically.
   3 %
   4 \ifx\havemjoarrow\undefined
   5 \def\havemjoarrow{1}
   6
   7
   8 \input{mjo-common} % for \of, at least.
   9
  10 \ifx\operatorname\undefined
  11   \usepackage{amsopn}
  12 \fi
  13
  14
  15 % The constant function that always returns its argument.
  16 \newcommand*{\const}[1]{\operatorname{const}_{{#1}}}
  17
  18 \ifdefined\newglossaryentry
  19   \newglossaryentry{const}{
  20     name={\ensuremath{\const{a}}},
  21     description={the constant function that always returns $a$},
  22     sort=c
  23   }
  24 \fi
  25
  26 % The identity function/arrow on its argument.
  27 \newcommand*{\identity}[1]{ \operatorname{id}_{{#1}} }
  28
  29 \ifdefined\newglossaryentry
  30   \newglossaryentry{identity}{
  31     name={\ensuremath{\identity{X}}},
  32     description={the identity function or arrow on $X$},
  33     sort=i
  34   }
  35 \fi
  36
  37 % The composition of two arrows/functions. For example, the
  38 % composition of g with f is \compose{g}{f}\of{x} === g\of{f\of{x}}.
  39 \newcommand*{\compose}[2]{ {#1}\circ{#2} }
  40
  41 % The inverse of an arrow, function, or whatever.
  42 \newcommand*{\inverse}[1]{ #1^{-1} }
  43
  44 % The preimage of the second argument (a set) under the first (a function).
  45 \newcommand*{\preimage}[2]{ #1^{-1}\of{#2} }
  46
  47
  48 \fi