groupoid
1Groupoid — dablink|This article is about groupoids in category theory. For the algebraic structure with a single binary operation see magma (algebra). In mathematics, especially in category theory and homotopy theory, a groupoid is a simultaneous… …
2groupoid — noun a) A magma: a set with a total binary operation. A groupoid is a category in which every morphism is an isomorphism. b) A set with a partial binary operation that is associative and has inverses and identities …
3groupoid — /grooh poyd/, n. Math. an algebraic system closed under a binary operation. Also called monoid. Cf. group (def. 9), semigroup. [GROUP + OID] * * * …
4groupoid — /grooh poyd/, n. Math. an algebraic system closed under a binary operation. Also called monoid. Cf. group (def. 9), semigroup. [GROUP + OID] …
5Double groupoid — In mathematics, especially in higher dimensional algebra and homotopy theory, a double groupoid generalises the notion of groupoid and of category to a higher dimension. Contents 1 Definition 2 Convolution algebra 3 Double Groupoid Category …
6Lie groupoid — In mathematics, a Lie groupoid is a groupoid where the set Ob of objects and the set Mor of morphisms are both manifolds, the source and target operations:s,t : Mor o Ob are submersions, and all the category operations (source and target,… …
7Lie algebroid — In mathematics, Lie algebroids serve the same role in the theory of Lie groupoids that Lie algebras serve in the theory of Lie groups: reducing global problems to infinitesimal ones. Just as a Lie groupoid can be thought of as a Lie group with… …
8Group action — This article is about the mathematical concept. For the sociology term, see group action (sociology). Given an equilateral triangle, the counterclockwise rotation by 120° around the center of the triangle acts on the set of vertices of the… …
9Ronald Brown (mathematician) — Ronald Brown, MA, D.Phil Oxon, FIMA, Emeritus Professor (born January 4, 1935) is an English mathematician. He is best known for his many, substantial contributions to Higher Dimensional Algebra and non Abelian Algebraic Topology, involving… …
10Equivalence relation — In mathematics, an equivalence relation is a binary relation between two elements of a set which groups them together as being equivalent in some way. Let a , b , and c be arbitrary elements of some set X . Then a b or a ≡ b denotes that a is… …
