nLab
coequalizer

Definition

In a category CC a diagram of morphisms of CC

UbaVcXU \underoverset{b}{a}{\rightrightarrows} V \overset{c}{\rightarrow} X

is called a coequalizer diagram if 1. ca=cbc a=c b; and 1. cc is universal for this property: i.e. if f:VYf: V \to Y is a morphism of CC such that fa=fbf a=f b, then there is a unique morphism f:XYf': X \to Y such that fc=ff'c=f.

This concept is a special case of that of colimit; specifically, it’s the colimit of the diagram

UbaV.U \underoverset{b}{a}{\rightrightarrows} V .

A coequalizer in CC is an equalizer in the opposite category C opC^{op}.

Revised on June 8, 2011 20:08:27 by Anonymous Coward (216.239.45.4)