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).

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Meanings

nounmonoidal category (plural monoidal categories)

plural monoidal categories

  1. category theoryA 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).
Cite this entry
APA

monoidal category. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/monoidal%20category

MLA

β€œmonoidal category.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/monoidal%20category. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. β€œmonoidal category,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/monoidal%20category.

Source: monoidal category on Wiktionary, CC BY-SA 4.0.