Results 11 to 20 of about 5,121 (158)
Crossed modules, double group-groupoids and crossed squares
Filomat, 2020 The purpose of this paper is to obtain the notion of crossed module over group-groupoids considering split extensions and prove a categorical equivalence between these types of crossed modules and double group-groupoids. This equivalence enables us to produce various examples of double groupoids.
Sedat Temel, Tunçar Şahan, Osman Mucuk
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Double groupoids and 2-groupoids in regular Mal'tsev categories [PDF]
Applied Categorical StructuresWe prove that the category 2-$ \mathrm{Grpd}(\mathscr{C}) $ of internal $2$-groupoids is a Birkhoff subcategory of the category $ \mathrm{Grpd}^2(\mathscr{C}) $ of double groupoids in a regular Mal'tsev category $\mathscr{C}$ with finite colimits. In particular, when $\mathscr{C}$ is a Mal'tsev variety of universal algebras, the category 2-$ \mathrm ...
Marino Gran, Nadja Egner
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Tensor categories and Vacant Double Groupoids [PDF]
Mathematical Research Letters, 2007 We show that fusion categories $\Rep(\ku^ _ \Tc)$ of representations of the weak Hopf algebra coming from a vacant double groupoid $\Tc$ and a pair $( , )$ of compatible 2-cocyles are group-theoretical.
Juan Martín Mombelli, Sonia Natale
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On slim double Lie groupoids [PDF]
Pacific Journal of Mathematics, 2012 15 ...
Nicolás Andruskiewitsch +2 more
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Double categories and quantum groupoids
, 2003 34 pages, amslatex.
Nicolás Andruskiewitsch, Sonia Natale
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The double algebraic view of finite quantum groupoids [PDF]
Journal of Algebra, 2004 48 pages, AMS ...
Kornél Szlachányi
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Discrete dynamical systems over double cross-product Lie groupoids
International Journal of Geometric Methods in Modern Physics, 2021 Discrete Euler–Lagrange equations are studied over double cross product Lie groupoids. As such, a geometric framework for the local analysis of a discrete dynamical system is established. The arguments are elucidated on the local discrete dynamics of a gauge groupoid. The discrete Elroy’s beanie is studied as a physical example.
Oğul Esen, Serkan Sütlü
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On symplectic double groupoids and the duality of Poisson groupoids [PDF]
International Journal of Mathematics, 1998 We prove that the cotangent of a double Lie groupoid S has itself a double groupoid structure with sides the duals of associated Lie algebroids, and double base the dual of the Lie algebroid of the core of S. Using this, we prove a result outlined by Weinstein in 1988, that the side groupoids of a general symplectic double groupoid are Poisson ...
Kirill C. H. Mackenzie
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A homotopy double groupoid of a hausdorff space [PDF]
Theory and Applications of Categories, 2002 Given a Hausdorff space \(X\), the authors construct a double groupoid called the homotopy double groupoid of \(X\). It is the cubical equivalent of the already known homotopy \(2\)-groupoid. The authors expect it to have the usual advantages of cubical structures for handling such things as van Kampen theorems and tensor products.
Ronald Brown +3 more
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Tensor categories attached to double groupoids [PDF]
Advances in Mathematics, 2004 The construction of a quantum groupoid out of a double groupoid satisfying a filling condition and a perturbation datum is given. This extends previous work that appeared in math.QA/0308228. Several important classes of examples of tensor categories are shown to fit into this construction.
Nicolás Andruskiewitsch, Sonia Natale
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