Related papers: Tambara functors
A functor on compact Hausdorf spaces is constructed as the sum of certain equivariant K-theory groups. It is shown that the functor takes values in lambda-rings and satisfies a Thom isomorphism. In the case that the space is a CW-complex…
Tambara modules are strong profunctors between monoidal categories. They've been defined by Tambara in the context of representation theory, but quickly found their way in applications when it was understood Tambara modules provide a useful…
The first word in the title is intended in a sense suggested by Lawvere and Schanuel whereby finite sets are objective natural numbers. At the objective level, the axioms defining abstract Mackey and Tambara functors are categorically…
Polynomial functors are useful in the theory of data types, where they are often called containers. They are also useful in algebra, combinatorics, topology, and higher category theory, and in this broader perspective the polynomial aspect…
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,…
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…
We derive a family of prime ideals of the Burnside Tambara functor for a finite group $G$. In the case of cyclic groups, this family comprises the entire prime spectrum. We include some partial results towards the same result for a larger…
We introduce a precise notion, in terms of few Schlessinger's type conditions, of extended deformation functors which is compatible with most of recent ideas in the Derived Deformation Theory (DDT) program and with geometric examples. With…
We define a functor which gives the "global rank of a quiver representation" and prove that it has nice properties which make it a generalization of the rank of a linear map. We demonstrate how to construct other "rank functors" for a…
We show that the free construction from multicategories to permutative categories is a categorically-enriched non-symmetric multifunctor. Our main result then shows that the induced functor between categories of algebras is an equivalence…
We provide a complete characterization of the equivariant commutative ring structures of all the factors in the idempotent splitting of the G-equivariant sphere spectrum, including their Hill-Hopkins-Ravenel norms, where G is any finite…
We prove a thick subcategory theorem for the category of $d$-excisive functors from finite spectra to spectra. This generalizes the Hopkins-Smith thick subcategory theorem (the $d=1$ case) and the $C_2$-equivariant thick subcategory theorem…
This is an attempt to extend to algebraic K-theory our approach to group actions in homological algebra that could be called an introduction to $\Gamma$-algebraic K-theory. For $\Gamma$-rings the Milnor algebraic K-theory and Swan's…
We give a broad study of representation and module theory of Rota-Baxter algebras. Regular-singular decompositions of Rota-Baxter algebras and Rota-Baxter modules are obtained under the condition of quasi-idempotency. Representations of an…
We enlarge the category of bornological coarse spaces by adding transfer morphisms and introduce the notion of an equivariant coarse homology theory with transfers. We then show that equivariant coarse algebraic $K$-homology and equivariant…
The category of rational G-equivariant cohomology theories for a compact Lie group $G$ is the homotopy category of rational G-spectra and therefore tensor-triangulated. We show that its Balmer spectrum is the set of conjugacy classes of…
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…
We introduce fusion algebras with not necessarily positive structure constants and without identity element. We prove that they are semisimple when tensored with $\mathbb{C}$ and that their characters satisfy orthogonality relations. Then…
We show that the algebraic K-theory of semi-valuation rings with stably coherent regular semi-fraction ring satisfies homotopy invariance. Moreover, we show that these rings are regular if their valuation is non-trivial. Thus they yield…
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…