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. © 2013 Elsevier B.V.
CITATION STYLE
Buckley, M. (2014). Fibred 2-categories and bicategories. Journal of Pure and Applied Algebra, 218(6), 1034–1074. https://doi.org/10.1016/j.jpaa.2013.11.002
Mendeley helps you to discover research relevant for your work.