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Does the dot $F \cdot G$ between two functors indicate composition in traditional Leibnizian order,or does it mean “$F$ followed by $G$”? Because if the former, I think the universal arrow ought to be instead $\alpha: (Ran_G G) \cdot G \Rightarrow G$.
Added Avery’s result about the Giry monad as an example.
It’s not a terribly friendly Idea section. ’Condense functor’ redirects to dense functor and from there one can reach dense subspace. But we have a page codense functor, so I’ll make it point there.
Added two references
Jirí Adámek, Lurdes Sousa, D-Ultrafilters and their Monads, (arXiv:1909.04950)
Andrei Sipos, Codensity and Stone spaces, (arXiv:1409.1370)
Added this example
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