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In a recent paper the quantum 2-sphere $S^2_q$ was described as a quantum complex manifold. Here we consider several copies of $S^2_q$ and derive their braiding commutation relations. The braiding is extended to the differential and to the…

q-alg · Mathematics 2009-10-28 Chong-Sun Chu , Pei-Ming Ho , Bruno Zumino

Based on the novel notion of `weakly counital fusion morphism', regular weak multiplier bimonoids in braided monoidal categories are introduced. They generalize weak multiplier bialgebras over fields and multiplier bimonoids in braided…

Category Theory · Mathematics 2019-07-08 Gabriella Böhm , José Goméz-Torrecillas , Stephen Lack

This paper presents a framework based on matrices of monoids for the study of coupled cell networks. We formally prove within the proposed framework, that the set of results about invariant synchrony patterns for unweighted networks also…

Multiagent Systems · Computer Science 2022-01-13 Pedro M. Sequeira , António P. Aguiar , João Hespanha

In this expository paper, we discuss and compare the notions of braided and coboundary monoidal categories. Coboundary monoidal categories are analogues of braided monoidal categories in which the role of the braid group is replaced by the…

Quantum Algebra · Mathematics 2009-05-01 Alistair Savage

We extend the theory of Sweeder's measuring comonoids to the framework of duoidal categories: categories equipped with two compatible monoidal structures. We use one of the tensor products to endow the category of monoids for the other with…

Category Theory · Mathematics 2020-05-05 Ignacio López Franco , Christina Vasilakopoulou

We discuss what it means for a symmetric monoidal category to be a module over a commutative semiring category. Each of the categories of (1) cartesian monoidal categories, (2) semiadditive categories, and (3) connective spectra can be…

Category Theory · Mathematics 2018-08-29 John D. Berman

We define a monoid structure on the set of $k$-equal arrangements and use this structure to define limits of braid arrangements. We compute the cohomology of the associated limits of rational models of the arrangements complex complements.…

Algebraic Topology · Mathematics 2012-11-27 Matthew S. Miller , Max Wakefield

This paper defines double fibrations (fibrations of double categories) and describes their key examples and properties. In particular, it shows how double fibrations relate to existing fibrational notions such as monoidal fibrations and…

Category Theory · Mathematics 2022-05-31 Geoffrey Cruttwell , Michael Lambert , Dorette Pronk , Martin Szyld

Braided-enriched monoidal categories were introduced in work of Morrison-Penneys, where they were characterized using braided central functors. Recent work of Kong-Yuan-Zhang-Zheng and Dell extended this characterization to an equivalence…

Category Theory · Mathematics 2022-09-02 Zachary Dell , Peter Huston , David Penneys

Braided monoidal categories arise naturally as centres of monoidal categories and have been the focus of much recent attention in both mathematics and physics. By suitably restricting the use of the exchange rule, we obtain a sequent…

Logic · Mathematics 2010-10-27 Jonathan A. Cohen , Craig A. Pastro

A general notion of operad is given, which includes as instances, the operads originally conceived to study loop spaces, as well as the higher operads that arise in the globular approach to higher dimensional algebra. In the framework of…

Category Theory · Mathematics 2007-05-23 Mark Weber

We show how the categorial approach to inverse monoids can be described as a certain endofunctor (which we call the partialization functor) of some category. In this paper we show that this functor can be used to obtain several recently…

Group Theory · Mathematics 2010-04-02 Ganna Kudryavtseva , Volodymyr Mazorchuk

Using constraints from supersymmetry and string perturbation theory, we determine the string loop corrections to the hypermultiplet moduli space of type II strings compactified on a generic Calabi-Yau threefold. The corresponding…

High Energy Physics - Theory · Physics 2009-11-11 Daniel Robles-Llana , Frank Saueressig , Stefan Vandoren

We generalize the classical operad pair theory to a new model for $E_\infty$ ring spaces, which we call ring operad theory, and establish a connection with the classical operad pair theory, allowing the classical multiplicative infinite…

Algebraic Topology · Mathematics 2024-09-17 Kailin Pan

After 1-point compactification, the collection of all unordered configuration spaces of a manifold admits a commutative multiplication by superposition of configurations. We explain a simple (derived) presentation for this commutative…

Algebraic Topology · Mathematics 2024-05-15 Oscar Randal-Williams

We use the theory of regular objects in tensor categories to clarify the passage between braided multiplicative unitaries and multiplicative unitaries with projection. The braided multiplicative unitary and its semidirect product…

Operator Algebras · Mathematics 2019-12-23 Ralf Meyer , Sutanu Roy

We give a description of unital operads in a symmetric monoidal category as monoids in a monoidal category of unital $\Lambda$-sequences. This is a new variant of Kelly's old description of operads as monoids in the monoidal category of…

Algebraic Topology · Mathematics 2024-11-26 J. P. May , Ruoqi Zhang , Foling Zou

We generalise the notions of semi-regularity, regularity, and bi-regularity to unitary solutions of the braided Pentagon equation in concrete W*-categories with semi-regular/regular/bi-regular braiding, and study their properties. We show,…

Operator Algebras · Mathematics 2014-11-18 David Buecher , Sutanu Roy

In this paper, we introduce the category of brace triples in a braided monoidal setting and prove that it is isomorphic to the category of s-Hopf braces, which are a generalization of cocommutative Hopf braces. After that, we obtain a…

Rings and Algebras · Mathematics 2025-04-15 José Manuel Fernández Vilaboa , Ramón González Rodríguez , Brais Ramos Pérez

Given a category with a bifunctor and natural isomorphisms for associativity, commutativity and left and right identity we do not assume that extra constraining diagrams hold. We introduce groupoids of coupling trees to describe a version…

Category Theory · Mathematics 2007-05-23 W. P. Joyce