Resumen de Homotopy theory of monoid actions via group actions and an Elmendorf style theorem

Mehmet Akif Erdal

• Let M be a monoid and be the group completion functor from monoids to groups. Given a collection of submonoids of M and for each a collection of subgroups of G(N), we construct a model structure on the category of M-spaces and M-equivariant maps, called the -model structure, in which weak equivalences and fibrations are induced from the standard -model structures on G(N)-spaces for all . We also show that for a pair of collections there is a small category whose objects are M-spaces for each and and morphisms are M-equivariant maps, such that the -model structure on the category of M-spaces is Quillen equivalent to the projective model structure on the category of contravariant -diagrams of spaces.