Monoidal category

This article defines a notion of a category along with some additional structure.
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Definition

A monoidal category is a category ${\mathcal {C}}$ equipped with an additional operation, called a monoidal operation:

$\otimes :\operatorname {Ob} {\mathcal {C}}\times \operatorname {Ob} {\mathcal {C}}\to \operatorname {Ob} {\mathcal {C}}$

satisfying the following conditions:

• Natural in both variables
• Has an identity upto natural isomorphism
• Associative upto natural isomorphism, where the natural isomorphism satisfies the pentagon axiom.