Fibred 2-categories and bicategories

Mitchell Buckley

doi:10.1016/j.jpaa.2013.11.002

Fibred 2-categories and bicategories

Mitchell Buckley^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

30 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	1034-1074
Number of pages	41
Journal	Journal of Pure and Applied Algebra
Volume	218
Issue number	6
DOIs	https://doi.org/10.1016/j.jpaa.2013.11.002
Publication status	Published - Jun 2014

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AB - 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.

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Fibred 2-categories and bicategories

Abstract

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