On the braiding on a Hopf algebra in a braided category.
Schauenburg, Peter (1998)
The New York Journal of Mathematics [electronic only]
Similarity:
Schauenburg, Peter (1998)
The New York Journal of Mathematics [electronic only]
Similarity:
Marco Grandis, Robert Paré (2012)
Diagrammes
Similarity:
Volodymyr Lyubashenko (1997)
Banach Center Publications
Similarity:
Given an abelian 𝑉-linear rigid monoidal category 𝑉, where 𝑉 is a perfect field, we define squared coalgebras as objects of cocompleted 𝑉 ⨂ 𝑉 (Deligne's tensor product of categories) equipped with the appropriate notion of comultiplication. Based on this, (squared) bialgebras and Hopf algebras are defined without use of braiding. If 𝑉 is the category of 𝑉-vector spaces, squared (co)algebras coincide with conventional ones. If 𝑉 is braided, a braided Hopf algebra can be obtained...
L. Montejano (1986)
Banach Center Publications
Similarity:
Majid, Shahn
Similarity:
[For the entire collection see Zbl 0742.00067.]The Tanaka-Krein type equivalence between Hopf algebras and functored monoidal categories provides the heuristic strategy of this paper. The author introduces the notion of a double cross product of monoidal categories as a generalization of double cross product of Hopf algebras, and explains some of the motivation from physics (the representation theory for double quantum groups).The Hopf algebra constructions are formulated in terms of...
Mara Alagić (1989)
Publications de l'Institut Mathématique
Similarity:
Julia E. Bergner, Philip Hackney (2015)
Fundamenta Mathematicae
Similarity:
We study a certain type of action of categories on categories and on operads. Using the structure of the categories Δ and Ω governing category and operad structures, respectively, we define categories which instead encode the structure of a category acting on a category, or a category acting on an operad. We prove that the former has the structure of an elegant Reedy category, whereas the latter has the structure of a generalized Reedy category. In particular, this approach gives a new...
Marco Riccardi (2015)
Formalized Mathematics
Similarity:
The main purpose of this article is to introduce the categorical concept of pullback in Mizar. In the first part of this article we redefine homsets, monomorphisms, epimorpshisms and isomorphisms [7] within a free-object category [1] and it is shown there that ordinal numbers can be considered as categories. Then the pullback is introduced in terms of its universal property and the Pullback Lemma is formalized [15]. In the last part of the article we formalize the pullback of functors...
Mara Alagić (1991)
Publications de l'Institut Mathématique
Similarity:
Bruguiéres, Alain, Virelizier, Alexis (2005)
Algebraic & Geometric Topology
Similarity: