The notion of normal subobject having an intrinsic meaning in any proto-modular category, we introduce the notion of normal functor, namely left exact conservative functor which reeects normal subobjects. The point is that for the category Gp of groups the change of base functors, with respect to the bration of pointed objects, are not only conservative (this is the deenition of a protomodular ...

The setting is the representation theory of a simply connected, semisimple algebraic group over a field of positive characteristic. There is a natural transformation from the wall-crossing functor to the identity functor. The kernel of this transformation is a left exact functor. This functor and its first derived functor are evaluated on the global sections of a line bundle on the flag variety...

Given a compact p-adic Lie group G over a finite unramified extension L/Qp let GL/Qp be the product over all Galois conjugates of G. We construct an exact and faithful functor from admissible G-Banach space representations to admissible locally L-analytic GL/Qp -representations that coincides with passage to analytic vectors in case L = Qp. On the other hand, we study the functor ”passage to an...

We provide explicit constructions for various ingredients of right exact monoidal structures on the category finitely presented functors. As our main tool, we prove a multilinear version universal property so-called Freyd categories, which in turn is used proof correctness constructions. Furthermore, compare construction with Day convolution arbitrary additive always yields closed structure all...

The Auslander correspondence is a fundamental result in Auslander-Reiten theory. In this paper we introduce the category modadm(E) of admissibly finitely presented functors and use it to give version for any exact E. An important ingredient proof localization theory categories. We also investigate how properties E are reflected modadm(E), example being (weakly) idempotent complete or having eno...

The notion of normal subobject having an intrinsic meaning in any protomodular category, we introduce the notion of normal functor, namely left exact conservative functor which reflects normal subobjects. The point is that for the category Gp of groups the change of base functors, with respect to the fibration of pointed objects, are not only conservative (this is the definition of a protomodul...

We show that derived equivalences preserve the homotopy type of the (cohomological) Hochschild complex as a B∞-algebra. More generally, we prove that, as an object of the homotopy category of B∞-algebras, the Hochschild complex is contravariant with respect to fully faithful derived tensor functors. We also show that the Hochschild complexes of a Koszul algebra and its dual are homotopy equival...

Orlov’s famous representability theorem asserts that any fully faithful exact functor between the bounded derived categories of coherent sheaves on smooth projective varieties is a Fourier-Mukai functor. This result has been extended by Lunts and Orlov to include functors from perfect complexes to quasi-coherent complexes. In this paper we show that the latter extension is false without the ful...

This paper is devoted to deformation theory of graded Lie algebras over Z or Zl with finite dimensional graded pieces. Such deformation problems naturally appear in number theory. In the first part of the paper, we use Schlessinger criteria for functors on Artinian local rings in order to obtain universal deformation rings for deformations of graded Lie algebras and their graded representations...

1 Belian categories 2 1.1 Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Pull-backs and push-outs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Ascent functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4 Snake Lemma . . . . . . . . . . . . . . . . . . . . . ....