Strict monomorphism
= Strict monomorphism
A <morphism> $m:A\to B$ is strict when every $g:C\to B$ satisfying $hm=km\Rightarrow hg=kg$ for all parallel arrows $h,k$ out of $B$ factors uniquely through $m$. Every <regular monomorphism> is strict by its <equalizer> property. A strict <monomorphism> is strong: in a lifting square with an <epimorphism>, cancellation of the <epimorphism> makes the bottom arrow admissible, and its unique factorization gives the diagonal.