Fibred 2-categories and bicategories

By Mitchell Buckley. 2012

70 citations recorded by the source corpus.

We generalise the usual notion of fibred category; first to fibred 2-categories and then to fibred bicategories. Fibred 2-categories correspond to 2-functors from a 2-category into 2Cat. Fibred bicategories correspond to trihomomorphisms from a bicategory into Bicat. We describe the Grothendieck construction for each kind of fibration and present a few examples of each. Fibrations in our sense, between bicategories, are closed under composition and are stable under equiv-comma. The free such fibration on a homomorphism is obtained by taking an oplax comma along an identity.

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/fe817fef8d9ae61a39b22e92d52c126527489403