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.

Revised on July 22, 2010 11:26:24 by Urs Schreiber (87.212.203.135)