Shadows for bicategories, defined by Ponto, provide a useful framework that generalizes classical and topological Hochschild homology. In this paper, we define Hochschild-type invariants for monoids in a symmetric monoidal, simplicial model category V, as ...
We compute the L-2-Betti numbers of the free C*-tensor categories, which are the representation categories of the universal unitary quantum groups A(u)(F). We show that the L-2-Betti numbers of the dual of a compact quantum group G are equal to the L-2-Bet ...
We prove that the category of rational SO(2)-equivariant spectra has a simple algebraic model. Furthermore, all of our model categories and Quillen equivalences are monoidal, so we can use this classification to understand ring spectra and module spectra v ...
Let X be a simplicial set. We construct a novel adjunction be- tween the categories RX of retractive spaces over X and ComodX+ of X+- comodules, then apply recent work on left-induced model category structures [5], [16] to establish the existence of a left ...
Lax monoidal powerset-enriched monads yield a monoidal structure on the category of monoids in the Kleisli category of a monad. Exponentiable objects in this category are identified as those Kleisli monoids with algebraic structure. This result generalizes ...
Let G be a finite group and R be a commutative ring. The Mackey algebra μR(G) shares a lot of properties with the group algebra RG however, there are some differences. For example, the group algebra is a symmetric algebra and this is not always the case fo ...
Kan spectra provide a combinatorial model for the stable homotopy category. They were introduced by Dan Kan in 1963 under the name semisimplicial spectra. A Kan spectrum is similar to a pointed simplicial set, but it has simplices in negative degrees as we ...
We exhibit sufficient conditions for a monoidal monad T on a monoidal category C to induce a monoidal structure on the Eilenberg-Moore category C^T that represents bimorphisms. The category of actions in C^T is then shown to be monadic over the base catego ...
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 commutative algebra ...
Sections are the building blocks of Wikipedia articles. They enhance readability and can be used as a structured entry point for creating and expanding articles. Structuring a new or already existing Wikipedia article with sections is a hard task for human ...
