Related papers: Mackey functors for posets
By homotopy linear algebra we mean the study of linear functors between slices of the $\infty$-category of $\infty$-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices…
Past studies of the Brauer group of a scheme tells us the importance of the interrelationship among Brauer groups of its finite \'etale coverings. In this paper, we consider these groups simultaneously, and construct an integrated object…
In this paper we compute $RO(G)$-graded homotopy Mackey functors of $H\underline{\mathbb{Z}}$, the Eilenberg-Mac Lane spectrum of the constant Mackey functor of integers for cyclic p-groups and give a complete computation for $G = C_{p^2}$…
We generalize the construction of reflection functors from classical representation theory of quivers to arbitrary small categories with freely attached sinks or sources. These reflection morphisms are shown to induce equivalences between…
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…
This note extends Quillen's Theorem A to a large class of categories internal to topological spaces. This allows us to show that under a mild condition a fully faithful and essentially surjective functor between such topological categories…
In this paper, we first introduce stable functors with respect to a preenveloping/precovering subcategory and investigate some of their properties. Using that we then introduce and study a relative complete cohomology theory in abelian…
Some basic features of the simultaneous inclusion of discrete fibrations and discrete opfibrations on a category A in the category of categories over A are studied; in particular, the reflections and the coreflections of the latter in the…
The purpose of this paper is mainly to record how certain homotopy-theoretical constructions on ordinary G-equivariant cohomology spectra HM for a Mackey functor M, in particular products and duality, can be described on chain level. We…
A poset is called upper homogeneous (or "upho") if every principal order filter of the poset is isomorphic to the whole poset. We observe that the rank and characteristic generating functions of upho posets are multiplicative inverses of…
We define the notion of {\em classifying space} of a topological stack and show that every topological stack \X has a classifying space X which is a topological space well-defined up to weak homotopy equivalence. Under a certain…
Rank functors on a quiver $Q$ are certain additive functors from the category of representations of $Q$ to the category of finite-dimensional vector spaces. Composing with the dimension function on vector spaces gives a rank function on…
The aim of the paper is to describe autocompact objects in Ab5-categories, i.e. objects in cocomplete abelian categories with exactness preserving filtered colimits of exact sequences, whose covariant Hom-functor commutes with copowers of…
A matching from a finite subset $A$ of an abelian group to another subset $B$ is a bijection $f:A\rightarrow B$ with the property that $a+f(a)$ never lies in $A$. A matching is called acyclic if it is uniquely determined by its multiplicity…
Suppose $G$ is a finite group. In this paper, we construct an equivalence between the $\infty$-category of algebras over an $N_{\infty}$-operad $\mathcal{O}$ associated to a $G$-indexing system $\mathcal{I}$ and the corresponding…
Among all states on the algebra of non-commutative polynomials, we characterize the ones that have monic orthogonal polynomials. The characterizations involve recursion relations, Hankel-type determinants, and a representation as a joint…
We give a specific cylinder functor for semifree dg categories. This allows us to construct a homotopy colimit functor explicitly. These two functors are "computable", specifically, the constructed cylinder functor sends a dg category of…
In this note we present examples of localization functors (in the category of spaces) whose composition with certain cellularization functors is not idempotent, and vice versa.
A poset can be regarded as a category in which there is at most one morphism between objects, and such that at most one of Hom(c,c') and Hom(c',c) is nonempty for distinct objects c,c'. If we keep in place the latter axiom but allow for…
For any object A in a simplicial model category M, we construct a topological space \^A which classifies homogeneous functors whose value on k open balls is equivalent to A. This extends a classification result of Weiss for homogeneous…