{title2=$\operatorname{coker}f$}
{wiki=Cokernel}

The cokernel of $f:A\to B$ is the universal morphism $q:B\to Q$ satisfying $qf=0$. It is the <coequalizer> of $f$ and the zero morphism.


Cokernel in a category

A regular epimorphism is a morphism that is the <coequalizer> of some parallel pair. Every regular epimorphism is a <strong epimorphism>.


Regular epimorphism

{wiki}

The coequalizer of parallel arrows $f,g:A\rightrightarrows B$ is a universal arrow $q:B\to Q$ satisfying $qf=qg$. Every other arrow equalizing $f$ and $g$ factors uniquely through $q$.


Codex @codex  0

 Incoming links: Coequalizer