Noun
(algebra) A magma: a set with a total binary operation.
(algebra and category theory) A set with a partial binary operation that is associative and has identities and inverses.
Source: en.wiktionary.orgA groupoid is a category in which every morphism is an isomorphism. Source: Internet
A groupoid can be seen as a: * Group with a partial function replacing the binary operation ; * Category in which every morphism is invertible. Source: Internet
Examples Linear algebra Given a field K, the corresponding general linear groupoid GL * (K) consists of all invertible matrices whose entries range over K. Matrix multiplication interprets composition. Source: Internet
Further the stabilizers of the action are the vertex groups, and the orbits of the action are the components, of the action groupoid. Source: Internet
Category of groupoids A subgroupoid is a subcategory that is itself a groupoid. Source: Internet
Given a groupoid in the category-theoretic sense, let G be the disjoint union of all of the sets G(x,y) (i.e. the sets of morphisms from x to y). Source: Internet