# nLab ambient category

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 ‘universe of discourse’, as when $C$ is a topos; see foundations.

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