An ambient category $C$ is just a category from which internal structures take their objects and structure morphisms.

If $C$ has extra structure, like being (semi-)abelian or a site, then one can do extra things; this is made precise through the concept of doctrine.

More generally an ambient category could be seen as a â€˜universe of discourseâ€™, as when $C$ is a topos; see foundations.

Last revised on June 11, 2009 at 02:09:46. See the history of this page for a list of all contributions to it.