Related papers: Polynomial functors over free nilpotent groups

The classical theory of free analysis generalizes the noncommutative (nc) polynomials and rational functions, easily providing such results as an nc analogue of the Jacobian conjecture. However, the classical theory misses out on important…

In this paper we extend categorically the notion of a finite nilpotent group to fusion categories. To this end, we first analyze the trivial component of the universal grading of a fusion category C, and then introduce the upper central…

Given a local ring containing a field, we define and investigate a family of invariants that includes the Lyubeznik numbers, but that captures finer information. These "generalized Lyubeznik numbers" are defined as lengths of certain…

In this article we extend evaluations of the Kauffman bracket on regular isotopy classes of knots and links to a variety of functors defined on the category of framed tangles. We show that many such functors exist, and that they correspond…

Consider the polynomial ring in countably infinitely many variables over a field of characteristic zero, together with its natural action of the infinite general linear group G. We study the algebraic and homological properties of finitely…

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…

In this article we study cohomological properties of the category of polynomial outer functors on free groups, which are the functors from the category of finitely generated free groups to the category of rational vector spaces which send…

Let $(A,\mathfrak{m})$ be a hypersurface local ring of dimension $d \geq 1$ and let $I$ be an $\mathfrak{m}$-primary ideal. We show that there is a non-negative integer $r_I$ (depending only on $I$) such that if $M$ is any non-free maximal…

Several adjunctions between functor categories have been studied and applied previously. These include Powell's adjunction between functor categories on free groups and on the linear PROP associated with the Lie operad, as well as those…

We consider maps between commutative groups and their functional degrees. These degrees are defined based on a simple idea -- the functional degree should decrease if a discrete derivative is taken. We show that the maps of finite…

We produce a fully faithful functor from finite type nilpotent spaces to cosimplicial binomial rings, thus giving an algebraic model of integral homotopy types. As an application, we construct an integral version of the…

Cohen proved that the infinite variable polynomial ring $R=k[x_1,x_2,\ldots]$ is noetherian with respect to the action of the infinite symmetric group $\mathfrak{S}$. The first two authors began a program to understand the…

Let R be the quotient of a polynomial ring over a field k by an ideal generated by monomials. We derive a formula for the multigraded Poincare' series of R, i.e., the generating function for the ranks of the modules in a minimal multigraded…

Working over an infinite field of positive characteristic, an upper bound is given for the nilpotency index of a finitely generated nil algebra of bounded nil index $n$ in terms of the maximal degree in a minimal homogenous generating…

This is an English translation of the author's Ph.D. thesis, accumulating his results on a construction of Cohen-Macaulay modules over a polynomial ring that appeared in the study of Cauchy-Fueter equations. This construction is generalized…

As shown in a previous paper by the same authors, the theory of Galois functors provides a categorical framework for the characterisation of bimonads on any category as Hopf monads and also for the characterisation of opmonoidal monads on…

We describe an abstract 2-categorical setting to study various notions of polynomial and analytic functors and monads.

A classification is provided of functors, in particular polynomial ones, from a category with a zero object in which every object is a finite sum of copies of a generating object, into an abelian category. This classification is extended to…

Let $A$ be a DG algebra with a trivial differential over a commutative unital ring. This paper investigates the image of the totaling functor, defined from the category of complexes of graded $A$-modules to the category of DG $A$-modules.…

Unstable operations in a generalized cohomology theory E give rise to a functor from the category of algebras over E to itself which is a colimit of representable functors and a comonoid with respect to composition of such functors. In this…