Related papers: Homotopical commutative rings and bispans

In their article "Elementary construction of perverse sheaves", R.MacPherson and K. Vilonen show that on a Thom-Mather space X the category PervX of perverse sheaves is equivalent to the category C(F, G, T) whose objects are data of…

We give a bicategorical version of the main result of A. Masuoka ({Corings and invertible bimodules,} {\em Tsukuba J. Math.} \textbf{13} (1989), 353--362) which proposes a non-commutative version of the fact that for a faithfully flat…

Let $G$ be a finite group. In [HTW], Hambleton, Taylor and Williams have considered the question of comparing Mackey functors for $G$ and biset functors defined on subgroups of $G$ and bifree bisets as morphisms. This paper proposes a…

We extend Goodwillie's classification of finitary linear functors to arbitrary small functors. That is we show that every small linear simplicial functor from spectra to simplicial sets is weakly equivalent to a filtered colimit of…

For a finite group $G$, a semi-Mackey (resp. Tambara) functor is regarded as a $G$-bivariant analog of a commutative monoid (resp. ring). As such, some naive algebraic constructions are generalized to this $G$-bivariant setting. In this…

We show that variants of the classical reflection functors from quiver representation theory exist in any abstract stable homotopy theory, making them available for example over arbitrary ground rings, for quasi-coherent modules on schemes,…

Let S be a commutative ring with topologically noetherian spectrum and let R be the absolutely flat approximation of S. We prove that subsets of the spectrum of R parametrise the localising subcategories of D(R). Moreover, we prove the…

We show that every small homotopy functor from spectra to spectra is weakly equivalent to a filtered colimit of representable functors represented in cofibrant spectra. Moreover, we present this classification as a Quillen equivalence of…

We study topological properties of the correspondence of prime spectra associated to a noncommutative ring homomorphism R -> S. Our main result provides criteria for the adjointness of certain functors between the categories of Zariski…

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…

As part of the study of correspondence functors, the present paper investigates their tensor product and proves some of its main properties. In particular, the correspondence functor associated to a finite lattice has the structure of a…

Since for the classification of finite (congruence-)simple semirings it remains to classify the additively idempotent semirings, we progress on the characterization of finite simple additively idempotent semirings as semirings of…

We prove that the classical result asserting that the relative Picard group of a faithfully flat extension of commutative rings is isomorphic to the first Amitsur cohomology group stills valid in the realm of symmetric monoidal categories.…

We construct reflection functors on categories of modules over deformed wreath products of the preprojective algebra of a quiver. These functors give equivalences of categories associated to generic parameters which are in the same orbit…

Let $G$ and $\check{G}$ be Langlands dual connected reductive groups. We establish a monoidal equivalence of $\infty$-categories between equivariant quasicoherent sheaves on the formal neighborhood of the nilpotent cone in $G$ and…

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…

Modular functors, i.e. consistent systems of projective representations of mapping class groups of surfaces, have been constructed for non-semisimple modular categories already decades ago. Concepts from homological algebra have not been…

We prove that TR is corepresentable by the reduced topological Hochschild homology of the flat affine line $\mathbf{S}[t]$ as a functor defined on the $\infty$-category of cyclotomic spectra with values in the $\infty$-category of spectra…

In this paper, we investigate the properties of the category of equivariant diagram spectra indexed on the category W_G of based G-spaces homeomorphic to finite G-CW-complexes for a compact Lie group G. Using the machinery of Mandell, May,…

We propose a generalization of Sullivan's de Rham homotopy theory to non-simply connected spaces. The formulation is such that the real homotopy type of a manifold should be the closed tensor dg-category of flat bundles on it much the same…