nLab
classifying morphism

Contents

Idea

A classifying map or classifying morphism for a given object is a morphism into a classifying space or moduli space that classified this object.

Typically this means that the map characterizes the object (only) up to equivalence. There is also the more refined concept of morphisms into a moduli stack that characterizes the object itself. For emphasis this case might be called a modulating morphism.

Examples

Revised on October 26, 2014 13:09:24 by Urs Schreiber (185.26.182.35)