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...

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

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

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...

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...

{\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...

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...

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

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...

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...

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

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

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...

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

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...

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

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...

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

axioms for groups, and may additionally use unary operations. Magma or groupoid: S and a single binary operation over S. Semigroup: an associative magma...

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

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...

arrangements: Weyl groupoids and simplicial arrangements, Bull. London Math. Soc. 43 (2011), no.4, 734-744. Cuntz, Heckenberger: Finite Weyl groupoids, J. Reine...

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...

This leads to the idea of modding out the gauge group to obtain the gauge groupoid as the closest description of the gauge connection in quantum field theory...

group with L G {\displaystyle {}^{L}G} . Wedhorn (2004) has established partial Tannaka duality results in the situation where the category is R-linear...