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Fibred 2-categories and bicategories

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arxiv 1212.6283 v2 pith:IBSRCIWC submitted 2012-12-27 math.CT

Mitchell Buckley This is my paper · ORCID
classification math.CT
keywords fibredbicategoriescategoriescategorycorrespondfibrationunderalong
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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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Cited by 1 Pith paper

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  1. From Grothendieck cofibrations to factorization systems: a formal 2-monadic account

    math.CT 2026-07 accept novelty 6.0 of 10

    Transport along a cofibration is converted, by a change of 2-monads, into the cocartesian–vertical factorization of arrows in the total category.

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