Related papers: Fused Mackey functors

An $F$-zip over a scheme $S$ over a finite field is a certain object of semi-linear algebra consisting of a locally free module with a descending filtration and an ascending filtration and a $\Frob_q$-twisted isomorphism between the…

Let $k$ be a field of characteristic $p>0$. Call a finite group $G$ a poco group over $k$ if any finitely generated cohomological Mackey functor for $G$ over $k$ has polynomial growth. The main result of this paper is that $G$ is a poco…

We show that differential calculus (in its usual form, or in the general form of topological differential calculus) can be fully imdedded into a functor category (functors from a small category of anchord tangent algebras to anchored sets).…

We give a functorial construction of equivariant spectra from a generalized version of Mackey functors in categories. This construction relies on the recent description of the category of equivariant spectra due to Guillou and May. The key…

We study the structure of the $RO(G)$-graded homotopy Mackey functors of any Eilenberg-MacLane spectrum $H\underline{M}$ for $G$ a cyclic $p$-group. When $\underline{R}$ is a Green functor, we define orientation classes $u_V$ for…

Let $R$ be an associative ring with unit. This paper deals with various aspects of the category of functors of $\mathcal R$-modules; that is, the category of additive and covariant functors from the category of R-modules to the category of…

Polynomial functors are a categorical generalization of the usual notion of polynomial, which has found many applications in higher categories and type theory: those are generated by polynomials consisting a set of monomials built from sets…

We examine the projective dimensions of Mackey functors and cohomological Mackey functors. We show over a field of characteristic $p$ that cohomological Mackey functors are Gorenstein if and only if Sylow $p$-subgroups are cyclic or…

Throughout this paper $G$ is a fixed group, and $k$ is a fixed field. All categories are assumed to be $k$-linear. First we give a systematic way to induce $G$-precoverings by adjoint functors using a 2-categorical machinery, which unifies…

Let $V$ be a M\"{o}bius vertex algebra and $G$ an abelian group of automorphisms of $V$. We construct $P(z)$-tensor product bifunctors for the category of $C_{n}$-cofinite grading-restricted generalized $g$-twisted $V$-modules (without…

Let $A$ be an algebra over a commutative ring $k$. We prove that braidings on the category of $A$-bimodules are in bijective correspondence to canonical R-matrices, these are elements in $A\ot A\ot A$ satisfying certain axioms. We show that…

Let M be a smooth manifold, and let O(M) be the poset of open subsets of M. Let C be a category that has a zero object and all small limits. A homogeneous functor (in the sense of manifold calculus) of degree k from O(M) to C is called very…

In this paper, we first construct some complete cotorson pairs on the category $\mathbb{C}_N(\mathcal{G})$ of unbounded $N$-complexes of Grothendieck category $\mathcal{G}$, from two given cotorsion pairs in $\mathcal{G}$. Next as an…

We describe the essential algebra, $\widehat{kB_T}(G)$, of the Burnside biset functor shifted by a group $T$, at a group $G$, in two cases. First, when $G$ and $T$ are both finite abelian groups and $k$ is a field of characteristic $0$. In…

In this paper we introduce the notion of a categorical Mackey functor. This categorical notion allows us to obtain new Mackey functors by passing to Quillen's $K$-theory of the corresponding abelian categories. In the case of an action by…

In this paper, we explain how the abstract notion of a differential bundle in a tangent category provides a new way of thinking about the category of modules over a commutative ring and its opposite category. MacAdam previously showed that…

This work concerns representations of a finite flat group scheme $G$, defined over a noetherian commutative ring $R$. The focus is on lattices, namely, finitely generated $G$-modules that are projective as $R$-modules, and on the full…

A pair of adjoint functors $(F,G)$ is called a Frobenius pair of the second type if $G$ is a left adjoint of $\beta F\alpha$ for some category equivalences $\alpha$ and $\beta$. Frobenius ring extensions of the second kind provide examples…

Let $R$ be a commutative Noetherian ring and let $\G$ be the category of modules of G-dimension zero over $R$. We denote the associated stable category by $\pG$. We show that the functor category $\modpG$ is a Frobenius category and we…

In this paper we extend equivariant infinite loop space theory to take into account multiplicative norms: For every finite group $G$, we construct a multiplicative refinement of the comparison between the $\infty$-categories of connective…