We introduce a new categorical framework for studying derived functors, and in particular for comparing composites of left and right derived functors. Our central observation is that model categories are the objects of a double category whose vertical and horizontal arrows are left and right Quillen functors, respectively, and that passage to derived functors is functorial at the level of this ...

The C*-algebra of bounded operators on the separable Hilbert space cannot be mapped to a W*-algebra in such a way that each unital commutative C*-subalgebra C(X) factors normally through `∞(X). Consequently, there is no faithful functor discretizing C*-algebras to W*-algebras this way.

This paper establishes two new connections between the familiar function ring functor ${mathfrak R}$ on the category ${bf CRFrm}$ of completely regular frames and the category {bf CR}${mathbf sigma}${bf Frm} of completely regular $sigma$-frames as well as their counterparts for the analogous functor ${mathfrak Z}$ on the category {bf ODFrm} of 0-dimensional frames, given by the integer-valued f...

As it is well known, torsion abelian groups are not preserved by localization functors. However, Libman proved that the cardinality of LT is bounded by |T |א0 whenever T is torsion abelian and L is a localization functor. In this paper we study localizations of torsion abelian groups and investigate new examples. In particular we prove that the structure of LT is determined by the structure of ...

It has been proven by Schupp and Bergman that the inner automorphisms of groups can be characterized purely categorically as those group coherently extended along any outgoing homomorphism. One is thus motivated to define a notion (categorical) automorphism in an arbitrary category, morphism, theory such forms part covariant isotropy. In this paper, we prove categorical category $$\textsf{Group...

Let ? be a commutative ring with involution ? containing an element ? such that ?+??=1 and let Alg?? the category of ?-algebras equipped semilinear preserving homomorphisms. We construct triangulated kkh functor jh:Alg???kkh is homotopy invariant, matricially hermitian stable excisive universal initial these properties. prove version Karoubi's fundamental theorem holds in kkh. By property latte...

Let G be a finite group, and R be a commutative ring. This note proposes a generalization to any Green functor for G over R of the construction of the Hochschild cohomology ring HH∗(G,R) from the ordinary cohomology functor H∗(−, R). Another special case is the construction of the crossed Burnside ring of G from the ordinary Burnside functor. The general abstract setting is the following : let ...