-
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
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...
- 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, a Lie
groupoid is a
groupoid where the set Ob {\displaystyle \operatorname {Ob} } of
objects and the set Mor {\displaystyle \operatorname...
- mathematics, a
quantum groupoid is any of a
number of
notions in
noncommutative geometry analogous to the
notion of
groupoid. In
usual geometry, the...
- this
sense is
called an isomorphism. A
groupoid is a
category in
which every morphism is an isomorphism.
Groupoids are
generalizations of groups, group...
- 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...
- {\displaystyle T^{*}M} is not
always integrable to a Lie
groupoid. A
symplectic groupoid is a Lie
groupoid G ⇉ M {\displaystyle {\mathcal {G}}\rightrightarrows...
- diffeomorphisms. An
orbifold groupoid is
given by one of the
following equivalent definitions: a
proper étale Lie
groupoid; a
proper Lie
groupoid whose isotropies...
