Fibred 2-categories and bicategories

Mitchell Buckley*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1034-1074
Number of pages41
JournalJournal of Pure and Applied Algebra
Issue number6
Publication statusPublished - Jun 2014


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