nLab flagged category




A flagged category consists of a category CC, a groupoid XX, and a surjection p:XCp \colon X\to C of groupoids from XX to the underlying groupoid of objects of CC (hence an essentially surjective functor).

One may also call this a category with an atlas, where the atlas is allowed to be groupoidal itself.

In type theory

A flagged category is a 1-truncated precategory.

See also


The terminology “flagged” for this notion appears (in generalization to higher category theory) in:

Last revised on September 18, 2022 at 04:27:51. See the history of this page for a list of all contributions to it.