Homotopy And Simple Homotopy Theory Find loads of the abstract homotopy and simple homotopy theory book catalogues in this site as the choice of you visiting this page. You can also join to the website book library that will show you numerous books from any types. Literature, science, politics, and many more catalogues are presented to offer you the best book to find. The book that really makes...

In this note we consider crossed modules of groups (N → G, G→ Aut(N)), as a homotopy version of the inclusion N ⊂ G of a normal subgroup. Our main observation is a characterization of the underlying map N → G of a crossed module, in terms of a simplicial group structure on the associated bar construction. This approach allows for “natural” generalizations to other monoidal categories, in partic...

For a finite quiver without sources or sinks, we prove that the homotopy category of acyclic complexes of injective modules over the corresponding finite-dimensional algebra with radical square zero is triangle equivalent to the derived category of the Leavitt path algebra viewed as a differential graded algebra with trivial differential, which is further triangle equivalent to the stable categ...

We construct a stable homotopy refinement of quantum annular homology, link homology theory introduced by Beliakova, Putyra and Wehrli. For each $r\geq 2$ we associate to an $L$ naive $\mathbb{Z}/r\mathbb{Z}$-equivariant spectrum whose cohomology is isomorphic the as modules over $\mathbb{Z}[\mathbb{Z}/r\mathbb{Z}]$. The construction relies on equivariant version Burnside category approach Laws...

The aim of this paper is to describe Quillen model category structures on the category CatC of internal categories and functors in a given finitely complete category C. Several non-equivalent notions of internal equivalence exist; to capture these notions, the model structures are defined relative to a given Grothendieck topology on C. Under mild conditions on C, the regular epimorphism topolog...

Spaces of maps into classifying spaces for equivariant crossed complexes, II: The general topological group case. Abstract The results of a previous paper [3] on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of homotopy coherence theory for cross...