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Category theory MOC

Bimonoid object

A bimonoid in a Symmetric monoidal category is at once a monoid and comonoid in a compatible way, consisting of the data

such that it is a comonoid in [[Category of monoid objects|]] or, what is the same, a monoid in . Unravelling definitions in terms of string diagrams, this gives the following compatibility conditions:

c

c

c

c

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