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James Deikun (May 07 2025 at 13:23):I have an area I'm looking at where there naturally appear fibrations over categories that don't necessarily have pullbacks or terminal objects. Various strange things happen in this situation, for example the identity functor doesn't have a (weak) generic object and the codomain "fibration" isn't a fibration at all. Are there any good resources on working with fibrations in this kind of limited environment?
Adittya Chaudhuri (May 11 2025 at 05:33):I do know whther it may be of any help, but I think [[differentiable stack]] are well studied examples of fibrations over a categorgy (here it is the category of smooth manifolds) that does not necessarily have pullbacks. One can represent them as Morita equivalent Lie groupoids.