plural of monoid

(mathematics) A set which is closed under an associative binary operation, and which contains an element which is an identity for the operation.

(prosody) Containing only one kind of metrical foot.

Of, pertaining to, or being a monoid.

With regard to monoids.

(psychology) The domination of a single idea, as in certain mental disorders

(psychology) Involving or dominated by a single idea.

plural of free monoid

(category theory) A category 𝒞 with a bifunctor ⊗:𝒞⨯𝒞→𝒞 which may be called tensor product, an associativity isomorphism 𝛼_(A,B,C):(A⊗B)⊗C≃A⊗(B⊗C), an object I which may be called tensor unit, a left unit natural isomorphism 𝜆_A:I⊗A≃A, a right unit natural isomorphism 𝜌_A:A⊗I≃A, and some "coherence conditions" (pentagon and triangle commutative diagrams for those isomorphisms).

(algebra) A monoid whose underlying set is the Kleene closure of some set of generators, and whose operator is concatenation.