Geodesic
Enriched model categories in equivariant contexts
Homology, homotopy, and applications, Tome 21 (2019) no. 1, pp. 213-246.

Voir la notice de l'article provenant de la source International Press of Boston

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 $\mathscr{V}$. For any $\mathscr{V}$, a discrete group $G$ gives a Hopf group, denoted $I[G]$. When $\mathscr{V}$ is cartesian monoidal, the Hopf groups are just the group objects in $\mathscr{V}$. When $\mathscr{V}$ 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 $\mathscr{V}$. This opens up some quite elementary unexplored mathematical territory, while systematizing more familiar terrain.
DOI : 10.4310/HHA.2019.v21.n1.a10
Classification : 55P91, 55U35
Keywords: enriched model category, equivariant model category, Hopf group 
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     title = {Enriched model categories in equivariant contexts},
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Bertrand Guillou; J.P. May; Jonathan Rubin. Enriched model categories in equivariant contexts. Homology, homotopy, and applications, Tome 21 (2019) no. 1, pp. 213-246. doi : 10.4310/HHA.2019.v21.n1.a10. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2019.v21.n1.a10/

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