Model Structures for Correspondences and Bifibrations

2018/07/22 by Stevenson, Danny
#18G55 (Secondary) #55U35 (Primary) 18G30 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.08226

Abstract

We study the notion of a bifibration in simplicial sets which generalizes the classical notion of two-sided discrete fibration studied in category theory. If A and B are simplicial sets we equip the category of simplicial sets over A× B with the structure of a model category for which the fibrant objects are the bifibrations from A to B. We also equip the category of correspondences of simplicial sets from A to B with the structure of a model category. We describe several Quillen equivalences relating these model structure with the covariant model structure on the category of simplicial sets over B^op× A.

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