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Patrick Nicodemus (Jan 03 2024 at 01:39):I'm pretty sure Grothendieck fibrations are algebras of a K Z monad. Anyone have a reference? I am particularly interested in like, 2 categorical fibrations or bicategorical fibrations but I'll take the 1 categorical case if that's all we have a reference for
Nathanael Arkor (Jan 03 2024 at 07:35):A reference is §3 of Street's Fibrations in bicategories.
Bryce Clarke (Jan 03 2024 at 08:45):I believe that Street's Fibrations and Yoneda's lemma in a 2-category is also a reference, but I do not have institutional access at the moment to check.
Matteo Capucci (he/him) (Jan 03 2024 at 09:00):IIRC it is also explained in one of the last chapters of Jacobs' book on categorical logic