nLab
trivial monoid
Context
Monoid theory
monoid theory in algebra:

monoid, infinitymonoid

monoid object, monoid object in an (infinity,1)category

Mon, CMon

monoid homomorphism

trivial monoid

submonoid, quotient monoid?

divisor, multiple?, quotient element?

inverse element, unit, irreducible element

ideal in a monoid

principal ideal in a monoid

commutative monoid

cancellative monoid

GCD monoid

unique factorization monoid

Bézout monoid

principal ideal monoid

group, abelian group

absorption monoid

free monoid, free commutative monoid

graphic monoid

monoid action

module over a monoid

localization of a monoid

group completion

endomorphism monoid

super commutative monoid
Contents
Definition
The trivial monoid is the unique (up to isomorphism) monoid with a single element  the neutral element of the monoid. The trivial monoid is also a terminal object and an initial object of Mon, making the trivial monoid a zero object of Mon.
See also
Last revised on March 17, 2023 at 16:15:47.
See the history of this page for a list of all contributions to it.