a groupoid object is both a generalization of a groupoid which is built on richer structures than sets, and a generalization of a group objects when...

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 mathematics, a Lie groupoid is a groupoid where the set Ob {\displaystyle \operatorname {Ob} } of objects and the set Mor {\displaystyle \operatorname...

mathematics, an ∞-groupoid is an abstract homotopical model for topological spaces. One model uses Kan complexes which are fibrant objects in the category...

constant sheaf. The fundamental groupoid of the singleton space is the trivial groupoid (a groupoid with one object * and one morphism Hom(*, *) = {...

binary operation. The word groupoid is used by many universal algebraists, but workers in category theory and related areas object strongly to this usage...

categories fibered in groupoids comes from groupoid objects internal to a category C {\displaystyle {\mathcal {C}}} . So given a groupoid object x ⇉ t s y {\displaystyle...

algebras can be seen as a generalization of group objects to monoidal categories. Groupoid object Awodey, Steve (2010), Category Theory, Oxford University...

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 one. Consider...

theory, a branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C, there exists precisely one morphism...