monoidal category

English

monoidal category (plural monoidal categories)

(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 and triangle commutative diagrams for those isomorphisms).

单词	monoidal category
释义	monoidal category English Noun monoidal category (plural monoidal categories) (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 and triangle commutative diagrams for those isomorphisms).
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