PlanetPhysics/Category of Borel Spaces

A category of Borel spaces has, as its objects, all Borel spaces , and as its morphisms the Borel morphisms between Borel spaces; the Borel morphism composition is defined so that it preserves the Borel structure determined by the -algebra of Borel sets.

The \htmladdnormallink{category {http://planetphysics.us/encyclopedia/Cod.html} of standard Borel G-spaces} is defined in a similar manner to , with the additional condition that Borel G-space morphisms commute with the Borel actions defined as Borel functions (or Borel-measurable maps). Thus, is a subcategory of ; in its turn, is a subcategory of --the category of topological spaces and continuous functions.

The category of rigid Borel spaces can be defined as above with the additional condition that the only automorphism (bijection) is the identity .