In abstract algebra, a magma, binar, or, rarely, groupoid is a basic kind of algebraic structure. Specifically, a magma consists of a set equipped with...

In mathematics, the concept of groupoid algebra generalizes the notion of group algebra. Given a groupoid ( G , ⋅ ) {\displaystyle (G,\cdot )} (in the...

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 abstract algebra, a partial groupoid (also called halfgroupoid, pargoid, or partial magma) is a set endowed with a partial binary operation. A partial...

In category theory, a branch of mathematics, an ∞-groupoid is an abstract homotopical model for topological spaces. One model uses Kan complexes which...

In algebraic topology, the fundamental groupoid is a certain topological invariant of a topological space. It can be viewed as an extension of the more...

category theory Higher-dimensional algebra Homological algebra K-theory Lie algebroid Lie groupoid Serre spectral sequence Sheaf Topological quantum field...

mentioned above. For example, a finite groupoid algebra is a weak Hopf algebra. In particular, the groupoid algebra on [n] with one pair of invertible arrows...

correspondence between Lie groups and Lie algebras, Lie groupoids are the global counterparts of Lie algebroids. Lie groupoids were introduced by Charles Ehresmann...

higher-dimensional algebra (HDA), a double groupoid is a generalisation of a one-dimensional groupoid to two dimensions, and the latter groupoid can be considered...