Fibred 2-categories and bicategories
Category Theory
2013-03-26 v2
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.
Cite
@article{arxiv.1212.6283,
title = {Fibred 2-categories and bicategories},
author = {Mitchell Buckley},
journal= {arXiv preprint arXiv:1212.6283},
year = {2013}
}
Comments
Changes to the introduction: gives a better description of how our work relates to the work of others. Added a few remarks