Matches in DBpedia 2014 for { ?s ?p In mathematics, especially in category theory and homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of group in several equivalent ways. A groupoid can be seen as a:Group with a partial function replacing the binary operation;Category in which every morphism is invertible. A category of this sort can be viewed as augmented with a unary operation, called inverse by analogy with group theory.Oriented graph Special cases include:Setoids, that is: sets that come with an equivalence relation;G-sets, sets equipped with an action of a group G.Groupoids are often used to reason about geometrical objects such as manifolds. Heinrich Brandt (1927) introduced groupoids implicitly via Brandt semigroups.. }
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- Groupoid abstract "In mathematics, especially in category theory and homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of group in several equivalent ways. A groupoid can be seen as a:Group with a partial function replacing the binary operation;Category in which every morphism is invertible. A category of this sort can be viewed as augmented with a unary operation, called inverse by analogy with group theory.Oriented graph Special cases include:Setoids, that is: sets that come with an equivalence relation;G-sets, sets equipped with an action of a group G.Groupoids are often used to reason about geometrical objects such as manifolds. Heinrich Brandt (1927) introduced groupoids implicitly via Brandt semigroups.".