nLab
universally closed morphism

Contents

Idea

A universally closed morphism is a closed morphism all whose pullbacks are also closed.

Definition

Let CC be a category with pullbacks and with a notion of closed morphism which is stable under composition and contains all the isomorphisms.

A morphism f:XYf:X\to Y in CC is universally closed if for every h:ZYh: Z\to Y the pullback h *(f):Z× YXZh^*(f): Z\times_Y X\to Z is a closed morphism.

In particular, for h=id Yh=id_Y we see that a universally closed morphism is itself closed.

Examples

Revised on May 1, 2011 08:43:10 by Zoran Škoda (109.227.47.152)