Is there an example of a category, and a monomorphism $m:X\to Y$ between two objects such that $m$ is regular, but not extremal? (A monomorphism $m:X\to Y$ is said to be extremal if whenever $m=g\circ e$ with $e$ an epimorphism, then $e$ is an isomorphism.)
Regular, but not extremal monomorphism
Dominic van der Zypen
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