Results on the niteness of induced crossed modules are proved both algebraically and topologically Using the Van Kampen type theorem for the fundamen tal crossed module applications are given to the types of mapping cones of classifying spaces of groups Calculations of the cohomology classes of some nite crossed modules are given using crossed complex methods Introduction Crossed modules were i...

In this paper, we show that Goodwillie calculus, as applied to functors from stable homotopy to itself, interacts in striking ways with chromatic aspects of the stable category. Localized at a fixed prime p, let T (n) be the telescope of a vn self map of a finite S–module of type n. The Periodicity Theorem of Hopkins and Smith implies that the Bousfield localization functor associated to T (n)∗...

In the theory of operads we consider generalized symmetric power functors defined by sums of coinvariant modules. One observes classically that the symmetric functor construction provides an isomorphism from the category of symmetric modules to a split subcategory of the category of functors on dgmodules (if dg-modules form our ground category). The purpose of this article is to obtain a simila...

In [2] we constructed homological localizations of spaces, groups, and 17"modules; here we generalize those constructions to give "factorization systems" and "homotopy factorization systems" for maps in categories. In Section 2 we recall the definition and basic properties of factorization systems, and in Section 3 we give our first existence theorem (3.1)for such systems. It can be viewed as a...

in this paper we introduce a generalization of m-small modules and discuss about the torsion theory cogenerated by this kind of modules in category . we will use the structure of the radical of a module in  and get some suitable results about this class of modules. also the relation between injective hull in  and this kind of modules will be investigated in this article.   for a module  we show...