# Coincidence of two morphisms

Let $C$ be an arbitrary category, $X,Y\in Obj(C)$ and $$f:X\to Y,$$ $$g:X\to Y.$$ How to define coincidence of such morphisms?

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Are you referring to the equalizer (en.wikipedia.org/wiki/Equaliser_(mathematics) ) of $f$ and $g$? Not all categories have equalizers. –  Shaun Ault Jan 4 '13 at 1:22
Equality between arrows or objects of an abstract category is a primitive notion, just as composition of compatible arrows is a primitive notion. –  hardmath Jan 4 '13 at 1:35
Although I don't think this question is about equalizers, I'll try to post a working link. Yay, it worked! Just use the [name](url) syntax instead of bare URL. For other methods, see this post. –  user53153 Jan 4 '13 at 1:37
Sorry, here's a working link: en.wikipedia.org/wiki/Equaliser_(mathematics) –  Shaun Ault Jan 4 '13 at 1:41
@hardmath Copy into the answer box? –  user53153 Jan 6 '13 at 3:33