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...

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...

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...

the more restrictive notion of a stack in groupoids. An algebraic stack or Artin stack is a stack in groupoids X over the fppf site such that the diagonal...

In category theory, a branch of mathematics, a groupoid object is both a generalization of a groupoid which is built on richer structures than sets, and...

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

information of a groupoid can be contained in its monoidal category of representations (by a version of Tannaka–Krein duality), in its groupoid algebra or in the...

In abstract algebra, a central groupoid is an algebraic structure defined by a binary operation ⋅ {\displaystyle \cdot } on a set of elements that satisfies...

Graph algebra Incidence algebra Hecke algebra of a locally compact group Path algebra Groupoid algebra Stereotype algebra Stereotype group algebra Hopf...

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...

higher-dimensional algebra and homotopy theory, a double groupoid generalises the notion of groupoid and of category to a higher dimension. A double groupoid D is a...

being categories and groupoids. This leads on to the subject of higher-dimensional algebra which can be defined as the study of algebraic theories with partial...

the notion of algebraic stacks was defined by Michael Artin. One of the motivating examples of an algebraic stack is to consider a groupoid scheme ( R ...

Neumann algebras of a measurable equivalence relation and a measurable groupoid can be defined. These examples generalise von Neumann group algebras and the...

the category of groupoids. This theorem gives the transition from topology to algebra, in determining completely the fundamental groupoid π 1 ( X , A )...

types of algebraic structures are studied. Abstract algebra is primarily the study of specific algebraic structures and their properties. Algebraic structures...

Actually, in the view 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...

In abstract algebra, a partial algebra is a generalization of universal algebra to partial operations. partial groupoid field — the multiplicative inversion...

structure. If C is a group (thought of as a groupoid with a single object), then RC is the group algebra. If C is a monoid (thought of as a category with...

Nichols algebras, 2008. Heckenberger: Nichols Algebras (Lecture Notes), 2008 http://www.mi.uni-koeln.de/~iheckenb/na.pdf Heckenberger: The Weyl groupoid of...

In mathematics, an action groupoid or a transformation groupoid is a groupoid that expresses a group action. Namely, given a (right) group action X ×...

x)\simeq G} ⁠. More generally, a groupoid is any small category in which every morphism is an isomorphism. In a groupoid, the set of all morphisms in the...

Category theory Monoidal category Groupoid Group object Coalgebra Bialgebra Hopf algebra Magma object Torsion (algebra) Symbolic mathematics Finite field...

Algebra. Springer. pp. 21–83. doi:10.1007/978-3-642-99902-4_2. ISBN 978-3-642-99902-4. Brown, R. (1970). "Fibrations of groupoids" (PDF). J. Algebra....

Differential Geometry (Wiley Classics Library) Volume 1, 2. Wedge Product of Lie Algebra Valued One-Form groupoid of Lie-algebra valued forms at the nLab...