Comonoid object

Homomorphism of comonoid objects

Given comonoids 𝐶,𝐶′ in 𝖢, a morphism 𝑓 :𝐶 →𝐶′ is a comonoid homomorphism iff 𝑓𝐨𝐩 :𝐶′ →𝐶 is a homomorphism of monoid objects in 𝖢𝐨𝐩. cat Thus we have

and

These are the morphisms in Category of comonoid objects.

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