algebra, a partial groupoid (also called halfgroupoid, pargoid, or partial magma) is a set endowed with a partial binary operation. A partial groupoid is a...

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...

In abstract algebra, a magma, binar, or, rarely, groupoid is a basic kind of algebraic structure. Specifically, a magma consists of a set equipped with...

{\displaystyle T^{*}M} is not always integrable to a Lie groupoid. A symplectic groupoid is a Lie groupoid G ⇉ M {\displaystyle {\mathcal {G}}\rightrightarrows...

Actually, in the view of category the only difference between groupoid and group is that a groupoid may have more than one object but the group must have only...

of morphisms, the groupoid algebra is a direct sum of tensor products of group algebras and matrix algebras. Hopf algebra Partial group algebra Khalkhali...

In abstract algebra, a partial algebra is a generalization of universal algebra to partial operations. partial groupoid field — the multiplicative inversion...

of Lie groupoids that Lie algebras play in the theory of Lie groups: reducing global problems to infinitesimal ones. Indeed, any Lie groupoid gives rise...

a special case of a groupoid include: Whereas the notion of "free equivalence relation" does not exist, that of a free groupoid on a directed graph does...

1073/pnas.71.5.1952. PMC 388361. PMID 16592156. Alan L. T. Paterson (1999). "Groupoids, inverse semigroups, and their operator algebras", Springer, ISBN 0-8176-4051-7...