groupoid


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groupoid

(ˈɡruːpɔɪd)
n
(Mathematics) maths an algebraic structure consisting of a set with a single binary operation acting on it
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
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Let (G, +) be a groupoid. Then (RNQ(G), [symmetry]) is a group with identity element
Among the topics are the Atiyah-Singer cobordism invariance and the tangent groupoid, multiplicative ergodic theorems for transfer operators: towards the identification and analysis of coherent structures in non-autonomous dynamical systems, two proofs of Taubes' theorem on strictly ergodic flows, extremal higher co-dimension cycles of the space of complete conics, and a general solution to (free) deterministic equivalents.
The Weyl groupoid of [B.sub.q] is a groupoid, denoted [W.sub.q],
A groupoid S is called a left almost semigroup if it satisfies the following left invertive law, (ab)c = (cb)a, for all a, b, c [member of] S.
Abel Grassmann's groupoid abbreviated as an AG-groupoid is a groupoid whose element satisfies the left invertive law i.e (ab)c = (cb)a for all a,b,c [member of] S.
A groupoid is a small category in which all morphisms are invertible.
A nonempty set R with an m-ary operation f is called an m-ary groupoid and is denoted by (R, f) (see Dudek [24]).
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.
Then C(S)(e, f) = {(f, ([u.sub.2], [v.sub.1]), e)} and C(S) is a groupoid. It is therefore easy to see that any mapping C(E) [right arrow] C(S) is a Pos-equivalence.
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.