Let M be a monoid and G : Mon → Grp be the group completion functor from monoids to groups. Given a collection Z of submonoids of M and for each N ∈ Z a collection YN of subgroups of G(N), we construct a model structure on the category of M -spaces and M -equivariant maps, in which weak equivalences and fibrations are determined by the standard YN model structures on G(N)-spaces for all N ∈ Z. We also show that there is a small category O(Z,Y) such that, under mild conditions on Z and YN ’s… Expand

For spaces with a group action, we introduce Bredon cohomology with local (or twisted) coefficients and show that it is invariant under weak equivariant homotopy equivalence. We use this new… Expand

A Turing Machine (TM) is an abstract, synchronous, deterministic computer with a finite number of internal states. It operates on the set of infinite words, or tapes, over some finite alphabet,… Expand

This paper shows that some enlargements of the category of sets with semigroup actions and equivariant functions possess two idempotent endofunctors, and shows that up to homotopy these categories are equivalent to the usual category of Sets with Semigroup actions.Expand

The locally presentable and accessible categories is universally compatible with any devices to read, and can be searched hundreds of times for their chosen readings, but end up in harmful downloads.Expand