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

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

A flagged category is a 1-truncated precategory.

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

- David Ayala, John Francis, Def. 0.12 of:
*Flagged higher categories*, in:*Topology and Quantum Theory in Interaction*, Contemporary Mathematics**718**, AMS (2018) [arXiv:1801.08973, ISBN:978-1-4704-4941-4]

Last revised on September 18, 2022 at 08:27:51. See the history of this page for a list of all contributions to it.