= Solution
A <monomorphism> is a morphism $m:X\to Y$ such that $mu=mv$ implies $u=v$ for every pair $u,v:Z\to X$. Dually, an <epimorphism> $e:X\to Y$ satisfies $ue=ve\Rightarrow u=v$. A <regular epimorphism> is a <coequalizer> of some parallel pair. An <isomorphism> has a two-sided inverse.
For a <product in a category>, write $\Delta_A:A\to A\times A$ for its <categorical diagonal>. Since $\pi_1\Delta_A=1_A$, equality $\Delta_Au=\Delta_Av$ gives $u=\pi_1\Delta_Au=\pi_1\Delta_Av=v$. Thus \b[the diagonal is a monomorphism], indeed a <split monomorphism>.
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