A morphismMathworldPlanetmath f:AB in a category is an isomorphismMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath if there exists a morphism f-1:BA which is its inverseMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath. The objects A and B are isomorphic if there is an isomorphism between them.

A morphism which is both an isomorphism and an endomorphism is called an automorphism. The set of automorphisms of an object A is denoted Aut(A).


Title isomorphism
Canonical name Isomorphism
Date of creation 2013-03-22 12:19:20
Last modified on 2013-03-22 12:19:20
Owner djao (24)
Last modified by djao (24)
Numerical id 6
Author djao (24)
Entry type Definition
Classification msc 54A05
Classification msc 15A04
Classification msc 13A99
Classification msc 20A05
Classification msc 18A05
Defines isomorphic
Defines automorphism