Word Pronunciation & Dictionary

monoidal category

Word Rarity Very rare

Frequency: Zipf frequency 1.32 in modern English

Syllables: monoidal -cat-e-go-ry
IPA

25

Scrabble Score

16

Letters

5

Syllables

13

Unique Chars

Meaning

noun

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).

Inflected Forms

monoidal categories (plural)

Questions

What does monoidal category mean?: 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).

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