Fibred 2-categories and bicategories |
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Authors: | Mitchell Buckley |
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Institution: | Department of Computing, Macquarie University, NSW 2109, Australia |
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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 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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Keywords: | 18D30 18D05 |
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