nLab
effective monomorphism

Context

Category theory

Higher category theory

higher category theory

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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 ff may probably also be called an embedding.

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

Last revised on July 22, 2010 at 11:26:24. See the history of this page for a list of all contributions to it.