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.