groupoid oor Nederlands
groupoid
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(algebra) A magma: a set with a total binary operation.
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category where every morphism is invertible; generalization of a group
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categorietheorie
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They arise in the study of more complicated forms of symmetry, often in topological and analytical structures, such as the fundamental groupoid or stacks.
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A groupoid can be seen as a: Group with a partial function replacing the binary operation; Category in which every morphism is invertible.
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It was introduced by Vladimir Drinfeld (1990) and named after Alexander Grothendieck and Oswald Teichmüller, based on Grothendieck's suggestion in his Esquisse d'un Programme to study the absolute Galois group of the rationals by relating it to its action on the Teichmüller tower of Teichmüller groupoids Tg,n, the fundamental groupoids of moduli stacks of genus g curves with n points removed.
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In abstract algebra, a magma (or groupoid; not to be confused with groupoids in category theory) is a basic kind of algebraic structure.
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A category of this sort can be viewed as augmented with a unary operation, called inverse by analogy with group theory.[1] Notice that a groupoid where there is only one object is a usual group.
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Groupoids are often used to reason about geometrical objects such as manifolds.
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Working with Professor Rui Loja Fernandes, he solved a long-standing problem of generalising Sophus Lie’s third theorem from the setting of Lie groups (every Lie algebra is associated with a Lie group) to that of Lie groupoids.
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A groupoid can be seen as a:
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They arise in the study of more complicated forms of symmetry, often in topological and analytical structures, such as the fundamental groupoid or stacks.
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Groupoids are similar to groups except that the composition a • b need not be defined for all a and b.
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