Free $K$ -comonoid

Let $𝑆$ be a inhabited set. The free $K$ -comonoid $K (𝑆)$ is the corresponding free module with the additional structure of an $K$ -comonoid given by

Δ (𝑠) = 𝑠 \otimes 𝑠, 𝜖 (𝑠) = 1

for all $𝑠 \in 𝑆$ .

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Free K-comonoid

Free $K$ -comonoid