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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:
Special cases include:
Groupoids are often used to reason about geometrical objects such as manifolds. Heinrich Brandt introduced groupoids implicitly via Brandt semigroups in 1926.^{[1]}
Contents
Definitions
Algebraic
A groupoid is a set G with a unary operation and a partial function * is not a binary operation because it is not necessarily defined for all possible pairs of Gelements. The precise conditions under which * is defined are not articulated here and vary by situation.
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