nLab
effective monomorphism

Effective monomorphisms

Context

Category theory

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Effective monomorphisms

Idea

Definition

A morphism f:XYf : X \to Y in a category CC is an effective monomorphism if

  1. it has a cokernel pair, i.e. if the pushout Y XYY \coprod_X Y exists;

  2. it is the equalizer of the canonical pair of morphisms YY XYY \stackrel{\to}{\to}Y \coprod_X Y.

Such a morphism, ff, may probably also be called an embedding.

The dual concept is that of effective epimorphism. See there for more discussion.

Last revised on August 8, 2020 at 05:16:33. See the history of this page for a list of all contributions to it.