nLab
coequalizer

Contents

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 October 14, 2014 03:51:43 by John Dougherty? (68.101.162.59)