Category theory MOC

Tensor product of (co)monoids

Let and be monoids in a Symmetric monoidal category with braiding . Then the tensor product is given the structure of a monoid where cat

up to application of the unitor and associator of . In terms of string diagrams,

By duality (turning the diagrams upside down), one gets the same construction for tensor product of comonoids: If and are comonoids then is given the structure of a comonoid where

up to application of the unitor and associator of .

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