Related papers: Weak bialgebras and monoidal categories

We study group algebras for compact groups in the category of real and complex weakly complete vector spaces. We also show that the group algebra is a quotient of the weakly complete universal enveloping algebra of the Lie algebra of the…

In [BaSc2], the author and Tomer Schlank introduced a much weaker homotopical structure than a model category, which we called a "weak cofibration category". We further showed that a small weak cofibration category induces in a natural way…

In this work, the partially and totally hom-coassociative ternary coalgebras are constructed and discussed. Their {infinitesimal} bialgebraic structures are also investigated. The related dual space structures and their properties are…

A compact space is said to be weakly Radon-Nikod\'{y}m (WRN) if it can be weak*-embedded into the dual of a Banach space not containing $\ell_1$. We investigate WRN Boolean algebras, i.e. algebras whose Stone space is WRN compact. We show…

We produce a cofibrantly generated simplicial symmetric monoidal model structure for the category of (small unital) C*-categories, whose weak equivalences are the unitary equivalences. The closed monoidal structure consists of the maximal…

The obstructions for an arbitrary fusion algebra to be a fusion algebra of some semisimple monoidal category are constructed. Those obstructions lie in groups which are closely related to the Hochschild cohomology of fusion algebras with…

We give a detailed comparison between the notion of a weak Hopf algebra (also called a quantum groupoid by Nikshych and Vainerman), and that of a $\times_R$-bialgebra due to Takeuchi (and also called a bialgebroid or quantum (semi)groupoid…

We first prove that every AF-algebra is weakly central, thereby resolving a question left open by Archbold--Gogi\'c. We then establish a new characterization of weak centrality for unital $C^*$-algebras in terms of $C(X)$-algebras. The…

With a view on applications in computing, in particular concurrency theory and higher-dimensional rewriting, we develop notions of $n$-fold monoid and comonoid objects in $n$-fold monoidal categories and bicategories. We present a series of…

We introduce the notion of a braiding on a skew monoidal category, whose curious feature is that the defining isomorphisms involve three objects rather than two. These braidings are shown to arise from, and classify, cobraidings (also known…

In this work we find Hochschild cohomology groups of the Weyl associative conformal algebra with coefficients in all finite modules. The Weyl conformal algebra is the universal associative conformal envelope of the Virasoro Lie conformal…

We introduce a notion of "weak model category" which is a weakening of the notion of Quillen model category, still sufficient to define a homotopy category, Quillen adjunctions, Quillen equivalences and most of the usual construction of…

Borger's theory of $\Lambda$-spaces imbues algebraic spaces, which include schemes, with an additional structure defined by an extension of the Witt vector functor. Motivated by $\mathbb{F}_1$-geometry, we prove the existence of a weak…

We describe (braided-)commutative algebras with non-degenerate multiplicative form in certain braided monoidal categories, corresponding to abelian metric Lie algebras (so-called Drinfeld categories). We also describe local modules over…

Let $A$ be an algebra over a commutative ring $k$. We compute the center of the category of $A$-bimodules. There are six isomorphic descriptions: the center equals the weak center, and can be described as categories of noncommutative…

In this paper we address the problem of classification of simple weight modules over weak generalized Weyl algebras of rank one. The principal difference between weak generalized Weyl algebras and generalized weight algebras is that weak…

This paper is a coalgebra version of arXiv:1703.04266 and a sequel to arXiv:1607.03066. We present the definition of a pseudo-dualizing complex of bicomodules over a pair of coassociative coalgebras $\mathcal C$ and $\mathcal D$. For any…

We introduce a general categorical framework for the definition of weak behavioural equivalences, building on and extending recent results in the field. This framework is based on parametrized saturation categories, i.e. categories whose…

As a step towards the structure theory of Lie algebras in symmetric monoidal categories we establish results involving the Killing form. The proper categorical setting for discussing these issues are symmetric ribbon categories.

We study the simplicial coalgebra of chains on a simplicial set with respect to three notions of weak equivalence. To this end, we construct three model structures on the category of reduced simplicial sets for any commutative ring R. The…