5.3.14 $\textbf{Rel}$ as a Category of Free Algebras

We have an isomorphism of categories

\[ \mathrm{Rel}\cong \mathsf{FreeAlg}_{\mathcal{P}_{*}}\webleft (\mathsf{Sets}\webright ), \]

where $\mathcal{P}_{*}$ is the powerset monad of .

Omitted.


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