monoidal categoryとは 意味・読み方・使い方

名詞

monoidal category (複数形 monoidal categories)

1. (category theory) A category ${\\displaystyle {\\mathcal {C}}}$ with a bifunctor ${\\displaystyle \\otimes :{\\mathcal {C}}\\times {\\mathcal {C}}\\rightarrow {\\mathcal {C}}}$ which may be called tensor product, an associativity isomorphism ${\\displaystyle \\alpha _{A,B,C}:(A\\otimes B)\\otimes C\\simeq A\\otimes (B\\otimes C)}$, an object ${\\displaystyle I}$ which may be called tensor unit, a left unit natural isomorphism ${\\displaystyle \\lambda _{A}:I\\otimes A\\simeq A}$, a right unit natural isomorphism ${\\displaystyle \\rho _{A}:A\\otimes I\\simeq A}$, and some "coherence conditions" (pentagon かつ triangle commutative diagrams for those isomorphisms).