Finding:

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   Groupoid

   Many concepts of group theory generalize to groupoids, with the notion of functor replacing that of group homomorphism. ... Shows how generalisations of Galois theory lead to Galois groupoids.
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   Ronald Brown (mathematician)

   From groups to groupoids: a brief survey, Bull. ... A common generalization for MV-algebras and Lukasiewicz-Moisil algebras, Archive for Mathematical Logic, Vol. 45, No. 8.
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   Lie groupoid

   A Lie groupoid can thus be thought of as a "many-object generalization" of a Lie group, just as a groupoid is a many-object generalization of a group. ... Lie groupoids
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   Higher-dimensional algebra

   Galois theories, F. Borceux, G. Janelidze, CUP, 2001, shows how generalisations of Galois theory lead to Galois groupoids.
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   Orbifold

   More sophisticated approaches use orbifold covering spaces or classifying spaces of groupoids. ... Ichirô Satake, On a generalization of the notion of manifold, Proc. Nat.
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   Equivalence relation

   Whereas the notion of "free equivalence relation" does not exist, that of a free groupoid on a directed graph does. ... Topology and Groupoids, Booksurge LLC.
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   Group (mathematics)

   An advanced generalization of this idea, adapted to the needs of algebraic geometry, is the étale fundamental group. ... Groupoids are similar to groups except that the composition a • b need not be defined for all a and b. They arise in the study of more complicated forms of symmetry, often in topological and analytical structures, such as the fundamental groupoid.
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   Symmetry

   This requires a generalization from the concept of symmetry group to that of a groupoid. ... The notion of groupoid also leads to notions of multiple groupoids, namely sets with many compatible groupoid structures, a structure which trivialises to abelian groups if one restricts to groups.
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   Galois theory

   Janelidze, G.; Borceux, Francis (2001), Galois theories, Cambridge University Press, ISBN 978-0-521-80309-0 (This book introduces the reader to the Galois theory of Grothendieck, and some generalisations, leading to Galois groupoids.)
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    Grothendieck's Galois theory

    Galois theories, ISBN 0521803098 (This book introduces the reader to the Galois theory of Grothendieck, and some generalisations, leading to Galois groupoids.)

Explore the following pages on Powerset:

• Groupoid,
• Ronald Brown (mathematician),
• Lie groupoid,
• Higher-dimensional algebra,
• Orbifold,
• Equivalence relation,
• Group (mathematics),
• Symmetry,
• Galois theory,
• Grothendieck's Galois theory