nLab
subquotient

Context

Limits and colimits

Category theory

Contents

Definition

A subquotient of an object XX in some category is

or

  • a subobject of a quotient object of XX.

Properties

  • The two definitions are equivalent whenever quotients are stable under pullback and subobjects are stable under pushout, such as in a topos.

  • Just as with subobjects and quotient objects, we have that XX is a subquotient of itself, and subquotients of subquotients of XX are themselves subquotients of XX in a natural way.

  • Just as subobjects of a set XX are in correspondence with predicates on XX and quotients of XX are in correspondence with equivalence relations on XX, subquotients of XX are in correspondence with partial equivalence relations on XX.

Examples

Revised on January 1, 2011 09:33:03 by Urs Schreiber (82.113.106.7)