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Some properties of Fib as a fibred 2-category

By Claudio Hermida

Abstract

AbstractWe consider some basic properties of the 2-category Fib of fibrations over arbitrary bases, exploiting the fact that it is fibred over Cat. We show a factorisation property for adjunctions in Fib, which has direct consequences for fibrations, e.g. a characterisation of limits and colimits for them. We also consider oplax colimits in Fib, with the construction of Kleisli objects as a particular example. All our constructions are based on an elementary characterisation of Fib as a 2-fibration

Publisher: Published by Elsevier B.V.
Year: 1999
DOI identifier: 10.1016/S0022-4049(97)00129-1
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