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Parametrized higher category theory

Jay Shah

Algebraic & Geometric Topology 23 (2023) 509–644
Abstract

We develop foundations for the theory of –categories parametrized by a base –category. Our main contribution is a theory of indexed homotopy limits and colimits, which specializes to a theory of G–colimits for G a finite group when the base is chosen to be the orbit category of G. We apply this theory to show that the G–category of G–spaces is freely generated under G–colimits by the contractible G–space, thereby affirming a conjecture of Mike Hill.

Keywords
parametrized higher category theory, equivariant homotopy theory
Mathematical Subject Classification 2010
Primary: 55U35, 55U40
Secondary: 55U10
References
Publication
Received: 18 July 2019
Revised: 21 October 2021
Accepted: 15 November 2021
Published: 9 May 2023
Authors
Jay Shah
Department of Mathematics and Computer Science
University of Münster
Münster
Germany

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