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...

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...

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...

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...

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

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...

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...

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...

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...

semigroups are fundamental models for linear time-invariant systems. In partial differential equations, a semigroup is associated to any equation whose...

composition, the collection of all partial one-one transformations of a set forms not an inverse semigroup but an inductive groupoid, in the sense of category...

like S1, the result follows from the groupoid Seifert-van Kampen theorem, as in the book Topology and Groupoids. More generally, McCord has shown that...

also considers a partial setoid using a partial equivalence relation or partial apartness (see e.g. Barthe et al., section 1). Groupoid Alexandre Buisse...

{\displaystyle \oplus } " for concatenation of paths in the fundamental groupoid and " ⊖ {\displaystyle \ominus } " for reversing the orientation of a path...

are orthogonal. In fact, small category is orthogonal to quasigroup, and groupoid is orthogonal to magma. Consequently there are zeros in R R T {\displaystyle...

inverse of G. The heap of a group may be generalized again to the case of a groupoid which has two objects A and B when viewed as a category. The elements of...

{\mathcal {F}}_{x}} where Π 1 X {\displaystyle \Pi _{1}X} is the fundamental groupoid of X: the category whose objects are points of X and whose morphisms are...

h-cobordisms form a groupoid. Then a finer statement of the s-cobordism theorem is that the isomorphism classes of this groupoid (up to C-isomorphism...

2, American Mathematical Society Clifford, Alfred. H. (1974), The Partial Groupoid of Idempotents of a Regular Semigroup, Tulane University, Department...

An ordered commutative monoid is a commutative monoid M together with a partial ordering ≤ such that a ≥ 0 for every a ∈ M, and a ≤ b implies a + c ≤ b...

semigroups in the same way that small categories generalise monoids and groupoids generalise groups. Semigroupoids have applications in the structural theory...

stack over differentiable manifolds which admits an atlas, or as a Lie groupoid up to Morita equivalence. Differentiable stacks are particularly useful...

{G}}} with an infinity groupoid. It is conjectured that the homotopy category of geometric realizations of infinity groupoids is equivalent to the homotopy...

With the same perspective, he pioneered the notions of jet and of Lie groupoid. Since the 1960s, Ehresmann's research interests moved to category theory...

automaton groupoid. Therefore, in the most general case, categories of variable automata of any kind are categories of groupoids or groupoid categories...

Lagrangian flow is a geodesic in a group of smooth transformations (see groupoid). It connects differential geometry of infinite-dimensional Lie groups...

two objects called the source and the target of the morphism. There is a partial operation, called composition, on the morphisms of a category that is defined...

factorial the complete elliptic integral of the third kind the fundamental groupoid osmotic pressure π {\displaystyle \pi } represents: Archimedes' constant...

2007) Distributions, Partial Differential Equations, and Harmonic Analysis (Universitext, Springer, 2013; 2nd ed., 2018) Groupoid Metrization Theory: With...