We study the category of discrete modules over the ring of degree zero stable operations in p-local complex K-theory. We show that the K(p)-homology of any space or spectrum is such a module, and that this category is isomorphic to a category defined by Bousfield and used in his work on the K(p)-local stable homotopy category [2]. We also provide an alternative characterisation of discrete modu...

The purpose of this paper is to investigate the homotopy theory of C*algebras of the formC0(X)⊗K, whereX is a finite connected CWcomplex with base point; hereC0(X) is theC*-algebra of continuous complex-valued functions which vanish at the base point, K is the C*-algebra of compact operators on a separable infinite dimensional complex Hilbert space, and a homotopy between two C*-algebra maps is...

Given a diagram of rings, one may consider the category of modules over them. We are interested in the homotopy theory of categories of this type: given a suitable diagram of model categories M(s) (as s runs through the diagram), we consider the category of diagrams where the object X(s) at s comes from M(s). We develop model structures on such categories of diagrams and Quillen adjunctions tha...

We show that the monoidal product on the stable homotopy category of spectra is essentially unique. This strengthens work of this author with Schwede on the uniqueness of models of the stable homotopy theory of spectra. Also, the equivalences constructed here give a unified construction of the known equivalences of the various symmetric monoidal categories of spectra (S-modules, W -spaces, orth...

The theory of local homology modules was initiated by Matlis in 1974. It is a dual version of the theory of local cohomology modules. Mohammadi and Divaani-Aazar (2012) studied the connection between local homology and Gorenstein flat modules by using Gorenstein flat resolutions. In this paper, we introduce generalized local homology modules for complexes and we give several ways for computing ...

The use of homological and homotopical devices, such as Tor and AndréQuillen homology, have found substantial use in characterizing commutative algebras. The primary category setting has been differentially graded algebras and modules, but recently simplicial categories have also proved to be useful settings. In this paper, we take this point of view up a notch by extending some recent uses of ...