:PROPERTIES:
:ID:       897bfc9d-94ce-4c58-8d21-93f13372b17b
:END:
#+title: Monomorphisms and epimorphisms

In [[id:90f23e03-f746-42cb-862f-1af2d4bde3cc][category theory]], *monomorphisms* and *epimorphisms* are types of cancellative morphisms generalising injective and surjective functions, respectively.[fn:1]

\begin{tikzcd}
% https://q.uiver.app/#q=WzAsNixbMCwwLCJYIl0sWzEsMCwiWSJdLFsyLDAsIloiXSxbMSwxLCJZIl0sWzIsMSwiWiJdLFswLDEsIlgiXSxbMCwxLCJnXzEiLDAseyJvZmZzZXQiOi0yfV0sWzAsMSwiZ18yIiwyLHsib2Zmc2V0IjoyfV0sWzEsMiwiZiIsMl0sWzMsNCwiZ18xIiwwLHsib2Zmc2V0IjotMn1dLFszLDQsImdfMiIsMix7Im9mZnNldCI6Mn1dLFs1LDMsImYiLDJdXQ==
	X & Y & Z \\
	X & Y & Z
	\arrow["{g_1}", shift left=2, from=1-1, to=1-2]
	\arrow["{g_2}"', shift right=2, from=1-1, to=1-2]
	\arrow["f"', from=1-2, to=1-3]
	\arrow["f"', from=2-1, to=2-2]
	\arrow["{g_1}", shift left=2, from=2-2, to=2-3]
	\arrow["{g_2}"', shift right=2, from=2-2, to=2-3]
\end{tikzcd}

* Footnotes

[fn:1] blahahahahah blah blah