monoidal categories

A form of monoidal category — 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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Meanings

noun
  1. pluralplural of monoidal category
Cite this entry
APA

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

MLA

“monoidal categories.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/monoidal%20categories. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “monoidal categories,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/monoidal%20categories.

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