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This article establishes the algebraic covering theory of quandles. For every connected quandle Q with base point q ∈ Q, we explicitly construct a universal covering p: (Q̃,q̃̃) → (Q,q). This in turn leads us to define the algebraic fundamental group $π ₁ (Q, q) : = A u t (p) = g \in A d j {(Q)}^{'} | q^{g} = q$ , where Adj(Q) is the adjoint group of Q. We then establish the Galois correspondence between connected coverings of (Q,q) and subgroups of π₁(Q,q). Quandle coverings are thus formally analogous to coverings of topological spaces, and resemble Kervaire’s...

Quantifying completion.

Lowen, Robert, Windels, Bart (2000)

International Journal of Mathematics and Mathematical Sciences

Quantizations in a category of relations.

Jakobsen, Per K., Lychagin, Valentin V. (2005)

Lobachevskii Journal of Mathematics

Quantizations of braided derivations. I: Monoidal categories.

Huru, H.L. (2006)

Lobachevskii Journal of Mathematics

Quantizations of braided derivations. II: Graded modules.

Huru, H.L. (2007)

Lobachevskii Journal of Mathematics

Quantizations of braided derivations. III: Modules with action by a group.

Huru, H.L. (2007)

Lobachevskii Journal of Mathematics

Quantum symmetries for exceptional $S U (4)$ modular invariants associated with conformal embeddings.

Coquereaux, Robert, Schieber, Gil (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Quasi locally connected toposes.

Bunge, Marta, Funk, Jonathon (2007)

Theory and Applications of Categories [electronic only]

Quasi resolved semigroups and quintets.

V.S. Krishnan (1979)

Semigroup forum

Quasi-abelian categories and sheaves

Jean-Pierre Schneiders (1999)

Mémoires de la Société Mathématique de France

Quasi-inverses of morphisms

Roman Sikorski (1974)

Fundamenta Mathematicae

Quasi-radicals and Radicals in Categories

A. Buys, S. Veldsman (1985)

Publications de l'Institut Mathématique

Quasi-reflections and limits

Ladislav Skula (1974)

Czechoslovak Mathematical Journal

Quasi-tilted algebras of canonical type

Helmut Lenzing, Andrzej Skowroński (1996)

Colloquium Mathematicae

Quasitriangular Hom-Hopf algebras

Yuanyuan Chen, Zhongwei Wang, Liangyun Zhang (2014)

Colloquium Mathematicae

A twisted generalization of quasitriangular Hopf algebras called quasitriangular Hom-Hopf algebras is introduced. We characterize these algebras in terms of certain morphisms. We also give their equivalent description via a braided monoidal category $̃ (_{H} ℳ)$ . Finally, we study the twisting structure of quasitriangular Hom-Hopf algebras by conjugation with Hom-2-cocycles.

Quasitriangular Hopf group algebras and braided monoidal categories

Shiyin Zhao, Jing Wang, Hui-Xiang Chen (2014)

Czechoslovak Mathematical Journal

Let $π$ be a group, and $H$ be a semi-Hopf $π$ -algebra. We first show that the category $_{H} ℳ$ of left $π$ -modules over $H$ is a monoidal category with a suitably defined tensor product and each element $α$ in $π$ induces a strict monoidal functor $F_{α}$ from $_{H} ℳ$ to itself. Then we introduce the concept of quasitriangular semi-Hopf $π$ -algebra, and show that a semi-Hopf $π$ -algebra $H$ is quasitriangular if and only if the category $_{H} ℳ$ is a braided monoidal category and $F_{α}$ is a strict braided monoidal functor for any $α \in π$ . Finally,...

Quasi-varieties of presheaves.

Vitale, Enrico M. (2000)

Theory and Applications of Categories [electronic only]

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