Related papers: Green correspondence on centric Mackey functor ove…

We develop the fundamentals of Mackey functors in the setup of fusion systems including an acyclicity condition as well as a parametrization and an explicit description of simple Mackey functors. Using this machinery we extend Dwyer's…

We study higher limits over the centric orbit category of a fusion system realized by an amalgamated product. In so doing we provide a novel technique for studying the Diaz-Park sharpness conjecture and prove it (in the case of the…

The box product of Mackey functors has been studied extensively in Lewis's notes. As shown in Thevenaz and Webb's paper, a Mackey functor may be identified with a module over a certain algebra, called the Mackey algebra. We aim at…

Systematically using the language of groupoids, we survey the theory of global Mackey functors, global Green functors and global power functors. Given a global power functor, we study rings with similar operations. The example of n-class…

We study the D\'iaz-Park sharpness conjecture for fusion systems and prove that, under certain circumstances, there exists a 4 terms exact sequence relating the first two higher limits of the contravariant part of a Mackey functor over…

We introduce the theory of biset functors defined on finite categories. Previously, biset functors have been defined on groups, and in that context they are closely related to Mackey functors. Standard examples on groups include…

We develop and extend the theory of Mackey functors as an application of enriched category theory. We define Mackey functors on a lextensive category $\E$ and investigate the properties of the category of Mackey functors on $\E$. We show…

We define and study the Burnside quotient Green ring of a Mackey functor. Some refinements of Dress induction theory are presented, together with applications to computation results for $K$-theory and $L$-theory of finite and infinite…

This note is motivated by the problem to understand, given a commutative ring F, which G-sets X, Y give rise to isomorphic F[G]-representations F[X]\cong F[Y]. A typical step in such investigations is an argument that uses induction…

We extend Dwyer's sharp subgroup homology decomposition of the classifying space of a finite group to arbitrary saturated fusion systems and arbitrary Mackey functors.

For a Green biset functor $A$, we define the commutant and the center of $A$ and we study some of their properties and their relationship. This leads in particular to the main application of these constructions: the possibility of splitting…

We say that a fusion system is the composition product of two subsystems if every morphism can be factored as a morphism in one fusion system followed by a morphism in the other. We establish a relationship between the characteristic…

A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commu-tative ring. A main tool for this study is the construction of a correspondence functor associated…

Let $C_n$ denote a cyclic group of order $n$. In this paper we investigate modules and chain complexes over the constant integral Mackey functor $\underline{\mathbb{Z}}$ and perform some related homological calculations. Along the way we…

We state and prove a fusion system version of Mislin's theorem \cite{Mislin1990} on cohomology and control of fusion, following Symonds's proof \cite{Symonds2004} of Mislin's theorem using Mackey functors.

We investigate correspondence functors, namely the functors from the category of finite sets and correspondences to the category of $k$-modules, where $k$ is a commutative ring.They have various specific properties which do not hold for…

Inspired by equivariant homotopy theory, equivariant algebra studies generalisations of G-Mackey functors that do not have all transfer maps (also known as induction maps), for G a finite group. These incomplete Mackey functors have…

We extend the theory of Mackey 2-functors introduced in arXiv:1808.04902 by defining the appropriate notion of rings, namely Green 2-functors. After providing the first results of our theory and abundant examples, we show how all classical…

Linking systems were introduced to provide algebraic models for $p$-completed classifying spaces of fusion systems. Every linking system over a saturated fusion system $\mathcal{F}$ corresponds to a group-like structure called a locality.…

We show that the passage from a $C^\ast$-correspondence to its Cuntz-Pimsner $C^\ast$-algebra gives a functor on a category of $C^\ast$-correspondences with appropriately defined morphisms. Applications involving topological graph…