Parametrized higher category theory

Shah, Jay

doi:10.2140/agt.2023.23.509

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Parametrized higher category theory

Jay Shah

Algebraic & Geometric Topology 23 (2023) 509–644

DOI: 10.2140/agt.2023.23.509

Abstract

We develop foundations for the theory of $\infty$ –categories parametrized by a base $\infty$ –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 $G$ – $\infty$ –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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Volume 23, issue 2 (2023)