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For a given twisted cartesian products of simplicial sets, we construct the corresponding twisted tensor product in the sense of Brown, with an explicit twisting function whose formula is simple without using inductions. This is done by…

Algebraic Topology · Mathematics 2026-04-13 Li Cai

The notion of quasicrossed product is introduced in the setting of G-graded quasialgebras, i.e., algebras endowed with a grading by a group G, satisfying a "quasiassociative" law. The equivalence between quasicrossed products and…

Rings and Algebras · Mathematics 2014-12-01 Helena Albuquerque , Elisabete Barreiro , José M. Sánchez-Delgado

We unify and generalize several approaches to constructing braid group representations from finite groups, using iterated twisted tensor products. Our results hint at a relationship between the braidings on the $G$-gaugings of a pointed…

Quantum Algebra · Mathematics 2019-06-20 Paul Gustafson , Andrew Kimball , Eric C. Rowell , Qing Zhang

We put two C*-algebras together in a noncommutative tensor product using quantum group coactions on them and a bicharacter relating the two quantum groups that act. We describe this twisted tensor product in two equivalent ways. The first…

Operator Algebras · Mathematics 2024-06-25 Ralf Meyer , Sutanu Roy , Stanislaw Lech Woronowicz

In this article we define the twisted product of groups as the generalization of the semidirect product of groups. We will find the necessary and sufficient condition in order that the twisted product of groups to be a group. In particular,…

dg-ga · Mathematics 2008-02-03 Michael A. Rudkovski

It is known that a category of many-sorted algebras on pure sets of similarity type is "concretely equivalent" to a category of single-sorted algebras. In this paper, we characterize a single-sorted variety that corresponds to a many-sorted…

Logic · Mathematics 2013-11-06 Shohei Izawa

One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we continue the work of [7] to adapt the machinery of globular operads [4] to…

Category Theory · Mathematics 2010-04-21 Michael Batanin , Denis-Charles Cisinski , Mark Weber

We define the phrase `category enriched in an fc-multicategory' and explore some examples. An fc-multicategory is a very general kind of 2-dimensional structure, special cases of which are double categories, bicategories, monoidal…

Category Theory · Mathematics 2007-05-23 Tom Leinster

Let $\mathfrak{g}$ be a Leibniz algebra and $E$ a vector space containing $\mathfrak{g}$ as a subspace. All Leibniz algebra structures on $E$ containing $\mathfrak{g}$ as a subalgebra are explicitly described and classified by two…

Rings and Algebras · Mathematics 2014-02-24 A. L. Agore , G. Militaru

Although the Cayley-Dickson algebras are twisted group algebras, little attention has been paid to the nature of the Cayley-Dickson twist. One reason is that the twist appears to be highly chaotic and there are other interesting things…

Rings and Algebras · Mathematics 2020-01-14 John Wayland Bales

The classical notion of twisted product is studied in the context of partial actions, in particular, we show that the globalization of a partial action is a twisted product. In addition, we establish conditions for the metrizability of…

General Topology · Mathematics 2024-01-04 Luis Martínez , Héctor Pinedo

We continue the study of enriched infinity categories, using a definition equivalent to that of Gepner and Haugseng. In our approach enriched infinity categories are associative monoids in an especially designed monoidal category of…

Category Theory · Mathematics 2021-07-06 V. Hinich

The comultiplication formula for fusion products of untwisted representations of the chiral algebra is generalised to include arbitrary twisted representations. We show that the formulae define a tensor product with suitable properties, and…

High Energy Physics - Theory · Physics 2009-10-30 M. R. Gaberdiel

Let $G$ be a group which admits a generating set consisting of finite order elements. We prove that any Hopf algebra which factorizes through the Taft algebra and the group Hopf algebra $K[G]$ (equivalently, any bicrossed product between…

Rings and Algebras · Mathematics 2019-08-27 A. L. Agore , L. Nastasescu

This paper introduces a skew variant of the notion of enriched category, suitable for enrichment over a skew-monoidal category, the main novelty of which is that the elements of the enriched hom-objects need not be in bijection with the…

Category Theory · Mathematics 2018-10-09 Alexander Campbell

We introduce a new notion of recursively generated enriched term which generalizes the one studied in joint work with Rosick\'y. These new terms come together with a notion of term-interpretability, which recovers the same type of…

Category Theory · Mathematics 2025-07-15 Giacomo Tendas

We detail a construction of a symmetric monoidal structure, called the reduced tensor product on the 2-category of braided tensor categories $\mathbf{BTC}(\mathcal{A})$ containing a fixed symmetric fusion subcategory $\mathcal{A}$. The…

Quantum Algebra · Mathematics 2024-04-15 Thomas A. Wasserman

Categorical bundles provide a natural framework for gauge theories involving multiple gauge groups. Unlike the case of traditional bundles there are distinct notions of triviality, and hence also of local triviality, for categorical…

Differential Geometry · Mathematics 2015-12-09 Saikat Chatterjee , Amitabha Lahiri , Ambar N. Sengupta

We introduce a definition of braided tensor product $\operatorname{M}\overline{\boxtimes}\operatorname{N}$ of von Neumann algebras equipped with an action of a quasi-triangular quantum group $\mathbb{G}$ (this includes the case when…

Operator Algebras · Mathematics 2024-12-24 Kenny De Commer , Jacek Krajczok

Twisted \'etale groupoid algebras have been studied recently in the algebraic setting by several authors in connection with an abstract theory of Cartan pairs of rings. In this paper, we show that extensions of ample groupoids correspond in…

Rings and Algebras · Mathematics 2021-01-26 Benjamin Steinberg