nLab
trivial monoid
Context
Monoid theory
monoid theory in algebra:
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monoid, infinity-monoid
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monoid object, monoid object in an (infinity,1)-category
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Mon, CMon
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monoid homomorphism
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trivial monoid
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submonoid, quotient monoid?
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divisor, multiple?, quotient element?
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inverse element, unit, irreducible element
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ideal in a monoid
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principal ideal in a monoid
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commutative monoid
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cancellative monoid
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GCD monoid
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unique factorization monoid
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Bézout monoid
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principal ideal monoid
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group, abelian group
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absorption monoid
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free monoid, free commutative monoid
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graphic monoid
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monoid action
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module over a monoid
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localization of a monoid
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group completion
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endomorphism monoid
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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.