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monoidal category

monoidal category noun: a category π’ž with a bifunctor βŠ—:π’žΓ—π’žβ†’π’ž which may be called tensor product, an associativity isomorphism Ξ±_(A,B,C):(AβŠ—B)βŠ—C≃AβŠ—(BβŠ—C), an object I which may be called tensor unit, a left unit natural isomorphism Ξ»_A:IβŠ—A≃A, a right unit natural isomorphism ρ_A:AβŠ—I≃A, and some "coherence conditions" (pentagon and triangle commutative diagrams for those isomorphisms).

Noun

monoidal category (plural monoidal categories)

  1. A category π’ž with a bifunctor βŠ—:π’žΓ—π’žβ†’π’ž which may be called tensor product, an associativity isomorphism Ξ±_(A,B,C):(AβŠ—B)βŠ—C≃AβŠ—(BβŠ—C), an object I which may be called tensor unit, a left unit natural isomorphism Ξ»_A:IβŠ—A≃A, a right unit natural isomorphism ρ_A:AβŠ—I≃A, and some "coherence conditions" (pentagon and triangle commutative diagrams for those isomorphisms).

Forms of monoidal category

pluralmonoidal categories

Questions about monoidal category

What does monoidal category mean?
Monoidal category means a category π’ž with a bifunctor βŠ—:π’žΓ—π’žβ†’π’ž which may be called tensor product, an associativity isomorphism Ξ±_(A,B,C):(AβŠ—B)βŠ—C≃AβŠ—(BβŠ—C), an object I which may be called tensor unit, a left unit natural isomorphism Ξ»_A:IβŠ—A≃A, a right unit natural isomorphism ρ_A:AβŠ—I≃A, and some "coherence conditions" (pentagon and triangle commutative diagrams for those isomorphisms).
What part of speech is monoidal category?
Monoidal category is a noun.
What is the plural of monoidal category?
The plural of monoidal category is monoidal categories.

Words near monoidal category in the dictionary

  1. monoicous
  2. monoicy
  3. monoid
  4. monoidal
  5. monoidal categories
  6. monoidal category
  7. monoidally
  8. monoideic
  9. monoideism
  10. monoideistic
  11. monoideological

Source and license

Adapted from Wiktionary: monoidal category (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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