Related papers: Strict polynomial functors and coherent functors
We study relation between left and right adjoint functors to the precomposition functor. As a cosnequence we obtain various dualities in the Ext-groups in the category of strict polynomial functors.
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…
Functorial semi-norms are semi-normed refinements of functors such as singular (co)homology. We investigate how different types of representability affect the (non-)triviality of finite functorial semi-norms on certain functors or classes.…
Given two quasi-definite moment functionals, the corresponding orthogonal polynomial systems satisfy an algebraic differential relation(called an extended coherent pair). We study generalizing extended coherent pairs that unify extended…
We investigate the structure of graded commutative exponential functors. We give applications of these structure results, including computations of the homology of the symmetric groups and of extensions in the category of strict polynomial…
We revisit faithfully balanced modules. These are faithful modules having the double centralizer property. For finite-dimensional algebras our main tool is the category ${\rm cogen}^1(M)$ of modules with a copresentation by summands of…
We identify a close relationship between stable sheaf cohomology for polynomial functors applied to the cotangent bundle on projective space, and Koszul--Ringel duality on the category of strict polynomial functors as described in the work…
We show in this work that homology in degree d of a congruence group, in a very general framework, defines a weakly polynomial functor of degree at most 2d and we describe this functor modulo polynomial functors of smaller degree. Our main…
The strict relation between some class of multiboson hamiltonian systems and the corresponding class of orthogonal polynomials is established. The correspondence is used effectively to integrate the systems. As an explicit example we…
We systematically develop the theory of definable functors between compactly generated triangulated categories. Such functors preserve pure triangles, pure injective objects, and definable subcategories, and as such appear in a wide range…
We study polynomial functors in the incompressible category $\text{Ver}_4^+$, which can be viewed as super polynomial functors in characteristic 2. Concretely, we classify additive, exact and simple polynomial functors, and describe how…
We give some functorial characterizations of flat strict Mittag-Leffler modules. We characterize reflexive functors of modules with similar tools, definitions and theorems.
We develop a new approach of extension calculus in the category of strict polynomial functors, based on Troesch complexes. We obtain new short elementary proofs of numerous classical Ext-computations as well as new results. In particular,…
Highest weight categories are described in terms of standard objects and recollements of abelian categories, working over an arbitrary commutative base ring. Then the highest weight structure for categories of strict polynomial functors is…
The aim of this paper is to study, by using the mathematical tools developed by Chalupnik, Touze, and Van der Kallen, the effect of the Frobenius twist on Ext-group in the category of strict polynomial functors. As an application, we obtain…
We study the integral torsion of the values of strict polynomial functors defined over the integers. We interpret some classical homological invariants as values of strict polynomial functors and therefore obtain estimates of the integral…
Prompted by an example related to the tensor algebra, we introduce and investigate a stronger version of the notion of separable functor that we call heavily separable. We test this notion on several functors traditionally connected to the…
We study the homological algebra in the category $\mathcal{P}_p$ of strict polynomial functors of degree $p$ over a field of positive characteristic $p$. We determine the decomposition matrix of our category and we calculate the Ext-groups…
We introduce the category of bicomodules for a comonad in a Grothendieck category whose underlying functor is right exact and preserves direct sums. We characterize comonads with a separable forgetful functor by means of cohomology groups…
We study selfadjoint functors acting on categories of finite dimensional modules over finite dimensional algebras with an emphasis on functors satisfying some polynomial relations. Selfadjoint functors satisfying several easy relations, in…