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arXiv · 1212.6283

Fibred 2-categories and bicategories

Mitchell Buckley
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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 2-Cat. 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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Mitchell Buckley. 2013-03-25. Fibred 2-categories and bicategories. https://arxiv.org/abs/1212.6283

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