Enriched model categories in equivariant contexts

Bertrand Guillou, J. P. May, Jonathan Rubin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We give a general framework of equivariant model category theory. Our groups G, called Hopf groups, are suitably defined group objects in any well-behaved symmetric monoidal category V . For any V, a discrete group G gives a Hopf group, denoted I[G]. When V is cartesian monoidal, the Hopf groups are just the group objects in V . When V is the category of modules over a commutative ring R, I[G] is the group ring R[G] and the general Hopf groups are the cocommutative Hopf algebras over R. We show how all of the usual constructs of equivariant homotopy theory, both categorical and model theoretic, generalize to Hopf groups for any V . This opens up some quite elementary unexplored mathematical territory, while systematizing more familiar terrain.

Original languageEnglish
Pages (from-to)213-246
Number of pages34
JournalHomology, Homotopy and Applications
Volume21
Issue number1
DOIs
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© 2018, International Press.

Keywords

  • Enriched model category
  • Equivariant model category
  • Hopf group

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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