#
Segal group actions

##
Matan Prasma

We define a model category structure on a slice category of
simplicial spaces, called the "Segal group action" structure, whose
fibrant-cofibrant objects may be viewed as representing spaces $X$
with an action of a fixed Segal group (i.e. a group-like, reduced
Segal space). We show that this model structure is Quillen
equivalent to the projective model structure on $G$-spaces,
$S^BG}$, where $G$ is a simplicial group corresponding to
the Segal group. One advantage of this model is that if we start
with an ordinary group action $X\in S^BG$ and apply a weakly
monoidal functor of spaces $L: S \to S$ (such as localization
or completion) on each simplicial degree of its associated Segal
group action, we get a new Segal group action of $LG$ on $LX$
which can then be rigidified via the above-mentioned Quillen
equivalence.

Keywords:
Model category, Segal space, group action, equivariant homotopy theory

2010 MSC:
55U35

*Theory and Applications of Categories,*
Vol. 30, 2015,
No. 40, pp 1287-1305.

Published 2015-09-24.

http://www.tac.mta.ca/tac/volumes/30/40/30-40.pdf

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