nLab extremal monomorphism

Definition

An extremal monomorphism in a category $C$ is a monomorphism $m$ such that if $m = g e$ where $e$ is an epimorphism, then $e$ is an isomorphism.

Remarks

The dual concept is extremal epimorphism, and all properties of extremal epimorphisms apply in the dual sense to extremal monomorphisms.

In Top the extremal monomorphisms coincide with the regular monomorphisms, and these are exactly the subspace embeddings.