Proposition 8.6.4.1.1 (02L4): Internal Monads in $\boldsymbol {\mathsf{Rel}}^{\mathord {\mathbin {\square }}}$

Table of Contents
Part 3: Relations
Chapter 8: Relations
Section 8.6: Properties of the 2-Category of Relations With Apartness Composition
Subsection 8.6.4: Internal Monads
Proposition 8.6.4.1.1: Internal Monads in $\boldsymbol {\mathsf{Rel}}^{\mathord {\mathbin {\square }}}$ (cite)

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8.6.4 Internal Monads

Let $X$ be a set.

Proposition 8.6.4.1.1 ▶ Internal Monads in $\boldsymbol {\mathsf{Rel}}^{\mathord {\mathbin {\square }}}$

We have a natural identification

\[ \left\{ \begin{gathered} \text{Monads in}\\ \text{$\boldsymbol {\mathsf{Rel}}^{\mathord {\mathbin {\square }}}$ on $X$} \end{gathered} \right\} \cong \left\{ \text{Subsets of $X$}\right\} . \]

Proof of Proposition 8.6.4.1.1.