Abstract
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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
–colimits
for
a finite group when the base is chosen to be the orbit category of
. We apply this theory to show that the
––category
of
–spaces is freely
generated under
–colimits
by the contractible
–space,
thereby affirming a conjecture of Mike Hill.
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Keywords
parametrized higher category theory, equivariant homotopy
theory
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Mathematical Subject Classification 2010
Primary: 55U35, 55U40
Secondary: 55U10
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Publication
Received: 18 July 2019
Revised: 21 October 2021
Accepted: 15 November 2021
Published: 9 May 2023
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| © 2023 The Author(s), under
exclusive license to MSP (Mathematical Sciences Publishers).
Distributed under the Creative Commons
Attribution License 4.0 (CC BY). |
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