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Wikipedia definition
1. Monoidal categoryIn mathematics, a monoidal category (or tensor category) is a category C equipped with a bifunctor ⊗ : C × C → C which is associative, up to a natural isomorphism, and an object I which is both a left and right identity for ⊗, again up to a natural isomorphism. (The associated natural isomorphisms are called natural because they together satisfy certain coherence conditions which state that all the relevant diagrams commute.
Read “Monoidal category” on English Wikipedia
Read “モノイド圏” on Japanese Wikipedia
Read “Monoidal category” on DBpedia

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