groupoid


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groupoid

[′grü‚pȯid]
(mathematics)
A set having a binary relation everywhere defined.
References in periodicals archive ?
A non-empty set of elements G is said to form a groupoid if in G is defined a binary operation called the product denoted by * such that a * b [member of] G, [for all] a, b [member of] G.
Keywords: frozen accident, rate distortion function, protein folding, free energy density, spin glass, groupoid, Onsager relations, holonomy
An Abel- Grassmann's groupoid, abbreviated as an AG-groupoid (or in some papers left almost semigroup), is a non-associative algebraic structure mid way between a groupoid and a commutative semigroup.
NIS TO R, Analysis ofgeometric operators on open manifolds: a groupoid approach, in Quantization of Singular Symplectic Quotients, N.
c], and they turn out to be automorphisms of the Einstein groupoid ([R.
Heller's current work focuses on the fields of noncommutative geometry and groupoid theory in mathematics.
Definition 1: An ordered pair (S, -), with S a non-empty set and - being a binary operation on S, is called a subtractive groupoid if (1.
By Theorem 5, P is a groupoid, where the inverse of a morphism [P] : T [right arrow] S is [[P.
Define a binary operation (*) on L: if x * y [member of] L for all x,y [member of] L, (L,*) is called a groupoid.
For example one may think of X/G as the groupoid whose set of objects is X and with morphisms given by X/G(a, b) = {g [member of] G|ga = b} for a,b [member of] G.
Keywords: global workspace, entropy, cognition, rate distortion function, giant component, groupoid, stochastic resonance.
Smarandache Groupoids exhibit simultaneously the properties of a semigroup and a groupoid.