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 cohomology to construct a Serre spectral sequence for equivariant fibrations. Bredon [1] introduced what is now called Bredon cohomology, with the purpose of developing obstruction theory in the context of ...

We propose a notion of 1-homotopy for generalized maps. This notion generalizes those of natural transformation and ordinary homotopy for functors. The 1-homotopy type of a Lie groupoid is shown to be invariant under Morita equivalence. As an application we consider orbifolds as groupoids and study the notion of orbifold 1-homotopy type induced by a 1-homotopy between presentations of the orbif...

Given a nite dimensional algebra over an algebraically closed eld one frequently disregards the projective objects in the category mod of nite dimensional-modules and focuses on the stable category mod. The objects of mod are those of mod but the Hom-groups are the ordinary Hom-groups modulo the subgroup of those morphisms which factor through a projective-module. In this paper we show that mod...

Let G be a locally compact group. We show that the category A(G) of actions of G on C∗-algebras (with equivariant nondegenerate ∗-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of maximal coactions of G under the comultiplication (C∗(G), δG); and also that A(G) is equivalent, via a reduced-crossed-product functor, to a comma catego...

We construct a model structure on the category $\mathrm{DblCat}$ of double categories and functors, whose trivial fibrations are functors that surjective objects, full horizontal vertical morphisms, fully faithful squares; fibrant objects weakly horizontally invariant categories. show functor $\mathbb H^{\simeq}\colon \mathrm{2Cat}\to \mathrm{DblCat}$, more homotopical version usual embedding H...

suspensions of A and attaching cones on suspensions of A (see [5, corollary 3.7]). If A = S, then a relative S–CW–complex is essentially an ordinary relative CW– complex. Any pointed map f : X → Y can be factored as a composition (X → Y ′ p → Y ), where (Y ′, X) is a relative A–CW–complex and p induces a weak equivalence of mapping spaces p? : map?(A, Y ′)→ map?(A, Y ). Let X be a pointed space...