Related papers: Functor homology over an additive category

We generalize the strong comparison theorem of Franjou, Friedlander, Scorichenko and Suslin to the setting of Fp-linear additive categories. Our results have a strong impact in terms of explicit computations of functor homology, and they…

We give sufficient conditions which ensure that a functor of finite length from an additive category to finite-dimensional vector spaces has a projective resolution whose terms are finitely generated. For polynomial functors, we study also…

We compare derived categories of the category of strict polynomial functors over a finite field and the category of ordinary endofunctors on the category of vector spaces. We introduce two intermediate categories: the category of…

In this paper we compute extension groups in the category of strict polynomial superfunctors and thereby exhibit certain "universal extension classes" for the general linear supergroup. Some of these classes restrict to the universal…

We prove a classification of additive polynomial superfunctors, which allows us to compute some extensions of a superfunctor of the form $F \circ A$ where $F$ is a classical polynomial functor and $A$ is additive. We get a formula which…

A relative derived category for the category of modules over a presheaf of algebras is constructed to identify the relative Yoneda and Hochschild cohomologies with its homomorphism groups. The properties of a functor between this category…

This article is a survey on the cohomology of a reductive algebraic group with coefficients in twisted representations. A large part of the paper is devoted to the advances obtained by the theory of strict polynomial functors initiated by…

We follow the same technics we used before in \cite{AZ} of extending knot Floer homology to embedded graphs in a 3-manifold, by using the Kauffman topological invariant of embedded graphs by associating family of links and knots to a such…

We explain how the approach of Andre and Quillen to defining cohomology and homology as suitable derived functors extends to generalized (co)homology theories, and how this identification may be used to study the relationship between them.…

The notion of a duality between two derived functors as well as an extension theorem for derived functors to larger categories in which they need not be defined is introduced. These ideas are then applied to extend and study the coext…

Let $R$ be a commutative ring with unit. We develop a Hochschild cohomology theory in the category $\mathcal{F}$ of linear functors defined from an essentially small symmetric monoidal category enriched in $R$-Mod, to $R$-Mod. The category…

We observe that there is an equivalence between the singularity category of an affine complete intersection and the homotopy category of matrix factorizations over a related scheme. This relies in part on a theorem of Orlov. Using this…

Let $k$ be an algebraically closed field of characteristic $p>0$, let $R$ be a commutative ring and let $\mathcal{F}$ be an algebraically closed field of characteristic $0$. We introduce the category $\overline{\mathcal{F}_{Rpp_k}}$ of…

We furnish any category of a universal (co)homology theory. Universal (co)homologies and universal relative (co)homologies are obtained by showing representability of certain functors and take values in $R$-linear abelian categories of…

We build an explicit link between coherent functors in the sense of Auslander and strict polynomial functors in the sense of Friedlander and Suslin. Applications to functor cohomology are discussed.

We introduce a new functor category: the category $\mathcal{P}_{d,n}$ of strict polynomial functors with bounded by $n$ domain of degree $d$ over a field of characteristic $p>0$. It is equivalent to the category of finite dimensional…

Given a group, we construct a fundamental additive functor on its orbit category. We prove that any isomorphism conjecture valid for this fundamental isomorphism functor holds for all additive functors, like K-theory, cyclic homology,…

Let $\k$ be a commutative ring, and let $(A,\mfrak{a})$ be an adic ring which is a $\k$-algebra. We study complete and torsion versions of the derived Hochschild homology and cohomology functors of $A$ over $\k$. To do this, we first…

For any additive functor from modules (or, more generally, from an abelian category with enough projectives or injectives), we construct long sequences tying up together the derived functors, the satellites, and the stabilizations of the…

In "Frobenius Categories versus Brauer Blocks" we have proved some universality of the so-called localizing functor associated with a Frobenius $P$-category $F$, where $P$ is a finite $p$-group, with respect to the coherent $F$-localities…