nLab
extremal monomorphism

Contents

Definition

An extremal monomorphism in a category CC is a monomorphism mm such that if m=gem = g e where ee is an epimorphism, then ee 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.

Revised on October 4, 2010 22:22:13 by Urs Schreiber (87.212.203.135)