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.

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.

Last revised on October 4, 2010 at 22:22:13. See the history of this page for a list of all contributions to it.