Systems theory deals with classes of identifiable parts each interacting in such a way that a given class exists together to satisfy certain specific requirements; these parts can be thought of an components of the system, some of which are permanent and some not. In analyzing a given system (see (13)) one usually offers up an m-tuple consisting of devices to be analyzed, pri-mitives to represe...

The program of categorification via category O was introduced by J. Bernstein, I. Frenkel, and M. Khovanov in [BFK] where tensor powers of the standard two dimensional representation of sl2 were recognized as Grothendieck groups of certain subcategories of O for various gln. They had two different constructions. One was based on studying certain blocks with singular generalized central characte...

We examine the projective dimensions of Mackey functors and cohomological Mackey functors. We show over a field of characteristic p that cohomological Mackey functors are Gorenstein if and only if Sylow p-subgroups are cyclic or dihedral, and they have finite global dimension if and only if the group order is invertible or Sylow subgroups are cyclic of order 2. By contrast, we show that the onl...

The behaviour under coarsening functors of simple, entire, or reduced graded rings, free modules over principal superfluous monomorphisms and homological dimensions modules, as well adjoints degree restriction functors, are investigated.

We provide an enhancement of Shipley's algebraicization theorem which behaves better in the context commutative algebras. This involves defining flat model structures as Shipley and Pavlov-Scholbach, showing that functors still Quillen equivalences this refined context. The use allows one to identify algebraic counterparts change groups functors, demonstrated forthcoming work author.

Bezrukavnikov and Etingof introduced some functors between the categories O for rational Cherednik algebras. Namely, they defined two induction functors Indb, indλ and two restriction functors Resb, resλ. They conjectured that one has functor isomorphisms Indb ∼= indλ,Resb ∼= resλ. The goal of this paper is to prove this conjecture.

A notion of a coring extension is defined and it is shown to be equivalent to the existence of an additive functor between comodule categories that factorises through forgetful functors. This correspondence between coring extensions and factorisable functors is illustrated by functors between categories of descent data. A category in which objects are corings and morphisms are coring extensions...

In the following note we characterize the category of Mackey-functors from a category ~, satisfying a few assumptions, to a category ~ as the category of functors from Sp(~), the category of "spans" in ~, to ~ which preserve finite products. This caracterization permits to apply all results on categories of functors preserving a given class of limits to the case of Mackey-functors. We recall (c...