Related papers: Strict polynomial functors and coherent functors
The category of strict polynomial functors inherits an internal tensor product from the category of divided powers. To investigate this monoidal structure, we consider the category of representations of the symmetric group which admits a…
We provide a unified framework for proving Reidemeister-invariance and functoriality for a wide range of link homology theories. These include Lee homology, Heegaard Floer homology of branched double covers, singular instanton homology, and…
We study higher Hochschild homology evaluated on wedges of circles, viewed as a functor on the category of free groups. The main results use coefficients arising from square-zero extensions; this is motivated by work of Turchin and…
In the first part of this note, we review and compare various instances of the notion of twisted coefficient system, a.k.a. polynomial functor, appearing in the literature. This notion hinges on how one defines the degree of a functor from…
By studying cohomology classes that are related with $p$-harmonic morphisms, $F$-harmonic maps, and $f$-harmonic maps, we extend several of our previous results on Riemannian submersions and $p$-harmonic morphisms to $F$-harmonic maps, and…
We introduce the notion of strong regular holonomic ${\mathcal{D}}_{{X\times S}/S}$-module and we prove that the functor ${\mathrm{RH}}^S$ introduced by T. Monteiro Fernandes and C. Sabbah in [14] takes image in…
We investigate the connection between left exact $\infty$-functors between finitely complete quasicategories and exact functors between fibration categories, describing a procedure to approximate flat $\infty$-functors of the former type by…
Let R be a commutative Noetherian ring, I and J ideals of R and M a finitely generated R-module. Let F be a covariant R-linear functor from the category of finitely generated R-modules to itself. We first show that if F is coherent, then…
Some general Finsler connections are defined. Emphasis is being made on the Cartan tensor and its derivatives. Vanishing of the hv-curvature tensors of these connections characterizes Landsbergian, Berwaldian as well as Riemannian…
We give analogues of the Auslander correspondence for two classes of triangulated categories satisfying certain finiteness conditions. The first class is triangulated categories with additive generators and we consider their endomorphism…
This article deals with computing the cohomology of Schur functors applied to tautological bundles on super Grassmannians. We show that in a range of cases, the cohomology is a free module over the cohomology of the structure sheaf and that…
In this paper we continue to investigate a certain class of Hankel-like positive definite kernels using their associated orthogonal polynomials. The main result of this paper is about the structure of this kind of kernels.
We restate the notion of orthogonal calculus in terms of model categories. This provides a cleaner set of results and makes the role of O(n)-equivariance clearer. Thus we develop model structures for the category of n-polynomial and…
The purpose of this article is threefold: Firstly, we propose some enhancements to the existing definition of 6-functor formalisms. Secondly, we systematically study the category of kernels, which is a certain 2-category attached to every…
Confirming a conjecture of Mark Shimozono, we identify polynomial representatives for the Schubert classes of the affine Grassmannian as the k-Schur functions in homology and affine Schur functions in cohomology. Our results rely on Kostant…
We introduce new concepts in order to develop a general formalism for twisted differential operators in several variables. We investigate the notion of twisted coordinates on Huber rings that allows us to build various rings of twisted…
We study finiteness properties, especially the noetherian property, the Krull dimension and a variation of finite presentation, in categories of polynomial functors from a small symmetric monoidal category whose unit is an initial object to…
We give an explicit formula to express the cohomological pullback functors of Hodge modules under closed immersions of smooth varieties using Verdier specializations and $V$-filtrations of Kashiwara and Malgrange. This was locally obtained…
We compute Ext-groups between classical exponential functors (i.e. symmetric, exterior or divided powers) and their Frobenius twists. Our method relies on bar constructions, and bridges these Ext-groups with the homology of Eilenberg-Mac…
This paper is concerned with a certain aspect of the spectral theory of unitary operators in a Hilbert space and its aim is to give an explicit construction of continuous functions of unitary operators. Starting from a given unitary…