Sorry about the slightly horrible language in the title. This question isn't so much about a mathematical problem, but about notation; I'm writing up some notes in TeX, and thought about this in connection with the $Hom(\cdot,\cdot)$ (bi-)functor, and while it is straight forward to write $Hom(x,y)$ for objects $x$ and $y$, I feel there isn't a good compact notation for morphisms. I've been using something kludgy like $Hom([x \xrightarrow{f} y],[w \xrightarrow{h} z])$. Isn't there something better?

  • 4
    $\begingroup$ What is wrong with $\mathrm {Hom}(f,h)$? It is also common to shorten things and write, for a category $\mathscr C$, $\mathscr C(x,y)$ instead of $\mathrm {Hom}_{\mathscr C}(x,y)$. $\endgroup$ Jul 11, 2018 at 13:50
  • 1
    $\begingroup$ Why not $\mathrm{Hom}(f, h)$ or $\mathrm{Hom}(f: x \to y, h: w \to z)$ if you need the objects? $\endgroup$ Jul 11, 2018 at 13:51
  • $\begingroup$ Nothing wrong - although, for $Hom(f,h)$, I will then have to specify domain and codomain separately. It all comes down to context, really; I just started wondering, when I really ought to have been doing something better with my time. $\endgroup$
    – j4nd3r53n
    Jul 12, 2018 at 13:37


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