Related papers: The Combinatorics of Polynomial Functors

Let $\mathbb C$ be the set of complex numbers, and let $\mathcal P$ be a collection of complex polynomial maps in several variables. Assuming at least one $P\in\mathcal P$ depends on at least two variables, we classify all possibilities for…

The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful;…

We classify the polynomials with integral coefficients that, when evaluated on a group element of finite order $n$, define a unit in the integral group ring for infinitely many positive integers $n$. We show that this happens if and only if…

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 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…

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…

We define tensors, corresponding to cubic polynomials, which have the same exponent $\omega$ as the matrix multiplication tensor. In particular, we study the symmetrized matrix multiplication tensor $sM_n$ defined on an $n\times n$ matrix…

We show that single-variable polynomial functors over the category $\mathcal{S}$ of infinity groupoids, as defined by Gepner-Haugseng-Kock, are exactly colimits of representable copresheaves indexed by infinity groupoid. This allows us to…

We show how the categorial approach to inverse monoids can be described as a certain endofunctor (which we call the partialization functor) of some category. In this paper we show that this functor can be used to obtain several recently…

In 1994, Long and Moody gave a construction on representations of braid groups which associates a representation of \mathbf{B}\_{n} with a representation of \mathbf{B}\_{n+1}. In this paper, we prove that this construction is functorial and…

We study the category $\mathcal{F}(\mathfrak{S}_S,\mathcal{V})$ of functors from the category $\mathfrak{S}_S$, which is the category of elements of some presheaf $S$ on the category $\mathcal{V}^f$ of finite dimensional vector spaces, to…

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…

We study polynomial comonads and polynomial bicomodules. Polynomial comonads amount to categories. Polynomial bicomodules between categories amount to parametric right adjoint functors between corresponding copresheaf categories. These may…

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…

For classical dynamical systems, the polynomial entropy serves as a refined invariant of the topological entropy. In the setting of categorical dynamical systems, that is, triangulated categories endowed with an endofunctor, we develop the…

We prove a generalisation to any characteristic of a result of Macdonald that describes strict polynomial functors in characteristic zero in terms of representations of the groupoid of finite sets and bijections. Our result will give an…

One can think of power series or polynomials in one variable, such as $P(x)=2x^3+x+5$, as functors from the category $\mathsf{Set}$ of sets to itself; these are known as polynomial functors. Denote by $\mathsf{Poly}_{\mathsf{Set}}$ the…

In this paper, we investigate how the initial models and the final models for the polynomial functors can be uniformly specified in matching logic.

Polynomial functors are useful in the theory of data types, where they are often called containers. They are also useful in algebra, combinatorics, topology, and higher category theory, and in this broader perspective the polynomial aspect…

This paper is concerned with the taxonomy of finitely complete categories, based on 'matrix properties' - these are a particular type of exactness properties that can be represented by integer matrices. In particular, the main result of the…