This entry is about semigroups with two-sided inverses. For semigroups with a unary operator such that and , see instead at inverse semigroup.
symmetric monoidal (∞,1)-category of spectra
geometric representation theory
representation, 2-representation, ∞-representation
Grothendieck group, lambda-ring, symmetric function, formal group
principal bundle, torsor, vector bundle, Atiyah Lie algebroid
Eilenberg-Moore category, algebra over an operad, actegory, crossed module
Be?linson-Bernstein localization?
A semigroup that is also an invertible magma.
An invertible semigroup is a semigroup such that for every element , left multiplication and right multiplication by are both bijections.
An invertible semigroup is a semigroup with a unary operation called the inverse such that
for all .
There is an alternate definition of an invertible semigroup that looks like the usual definition of a torsor or heap:
An invertible semigroup is a set with a binary operation called multiplication and a unary operation called inverse satisfying the following laws:
Every invertible semigroup has a pseudo-torsor, or associative Malcev algebras, defined as . If the invertible semigroup is inhabited, then those pseudo-torsors are actually torsors or heaps.
invertible magma (nonassociative version)
semigroup (non-invertible version)
group (unital version)
commutative invertible semigroup (commutative version)
possibly empty heap (forgetting the unit element)
Last revised on May 23, 2023 at 05:21:40. See the history of this page for a list of all contributions to it.