Fibred category theory is that part of category theory concerned with the study of fibred categories.
Fibred categories behave like (and, in a sense, are) categories parametrized by some other category or, put differently, like families of categories bundled together in a single object. Hence the 2-category of fibred categories over a fixed base has many formal analogies with the 2-category of categories, and this is one of the main focus of fibred category theory: to study the ‘category theory of fibred categories’.
Lots of fibred category theory is done at a higher level of generality, dealing with Street fibrations in any 2-category instead of specializing to Cat.
For the moment see the references at fibered category.
Last revised on October 18, 2023 at 13:27:21. See the history of this page for a list of all contributions to it.