Related papers: Some functors preserving exceptionality

We define and study a certain relative tensor product of subfactors over a modular tensor category. This gives a relative tensor product of two completely rational heterotic full local conformal nets with trivial superselection structures…

The tensor ideal localising subcategories of the stable module category of all, including infinite dimensional, representations of a finite group scheme over a field of positive characteristic are classified. Various applications concerning…

Let $B$ be a finite dimensional algebra and $A=B[P_0]$ be the one-point extension algebra of $B$ with respect to the finitely generated projective $B$-module $P_0$. The categories of $B$-modules and $A$-modules are related by two adjoint…

In this paper we continue the study of triangular matrix categories $\mathbf{\Lambda}=\left[ \begin{smallmatrix} \mathcal{T} & 0 \\ M & \mathcal{U} \end{smallmatrix}\right]$ initiated in [21]. First, given an additive category $\mathcal{C}$…

We study right exact tensor products on the category of finitely presented functors. As our main technical tool, we use a multilinear version of the universal property of so-called Freyd categories. Furthermore, we compare our constructions…

We develop methods for proving that certain extensions of polynomial functors do not split naturally. As an application we give a functorial description of the third and the fourth stable homotopy groups of the classifying spaces of free…

We study the category $\mathcal{O}$ for a general Coxeter system using a formulation of Fiebig. The translation functors, the Zuckerman functors and the twisting functors are defined. We prove the fundamental properties of these functors,…

In a previous paper we constructed rank and support variety theories for "quantum elementary abelian groups," that is, tensor products of copies of Taft algebras. In this paper we use both variety theories to classify the thick tensor…

We define exact functors from categories of Harish-Chandra modules for certain real classical groups to finite-dimensional modules over an associated graded affine Hecke algebra with parameters. We then study some of the basic properties of…

We study when induction functors (and their adjoints) between categories of Doi-Hopf modules and, more generally, entwined modules are separable, resp. Frobenius. We present a unified approach, leading to new proofs of old results by the…

For a quasi-compact quasi-separated scheme X and an arbitrary scheme Y we show that the pullback construction implements an equivalence between the discrete category of morphisms Y --> X and the category of cocontinuous tensor functors…

We characterize the regularity of an FI-module using the derivative functors.

We outline the theory of reflections for prederivators, derivators and stable derivators. In order to parallel the classical theory valid for categories, we outline how reflections can be equivalently described as categories of fractions,…

We establish a criterion for determining when a family of geometric functors is jointly conservative through the lens of purity in compactly generated triangulated categories. We introduce the notion of pure descendability and we apply it…

We consider a family of integer sequences generated by nonlinear recurrences of the second order, which have the curious property that the terms of the sequence, and integer multiples of the ratios of successive terms (which are also…

For any rigid presentation $e$, we construct an orthogonal projection functor to ${\rm rep}(e^\perp)$ left adjoint to the natural embedding. We establish a bijection between presentations in ${\rm rep}(e^\perp)$ and presentations compatible…

We study several structure aspects of functor categories from a small additive category to a module category, in particular the category F(A,K) of functors from finitely generated free modules over a commutative ring A to vector spaces over…

We construct the categories of standard vector bundles over schemes and define direct sum and tensor product. These categories are equivalent to the usual categories of vector bundles with additional properties. The tensor product is…

In this paper, we discuss certain circumstances in which the category of tame functors inherits an abelian category structure with minimal resolutions and a model category structure with minimal cofibrant replacements. We also present a…

In this note we consider different versions of coinduction functors between categories of comodules for corings induced by a morphism of corings. In particular we introduce a new version of the coinduction functor in the case of locally…