Homotopies in Grothendieck fibrations

Joseph Helfer

We define a natural 2-categorical structure on the base category of a large class of Grothendieck fibrations. Given any model category C, we apply this construction to a fibration whose fibers are the homotopy categories of the slice categories C/A, and we show that in the case C=Top, our construction applied to this fibration recovers the usual 2-category of spaces.

Keywords: Grothendieck fibrations, hyperdoctrine, 2-category

2020 MSC: Primary: 18D30. Secondary: 55U35

Theory and Applications of Categories, Vol. 35, 2020, No. 35, pp 1312-1378.

Published 2020-08-05.


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