Post #2044530

2026-04-29 17:48 UTC

@maxsnew Marcelo Fiore and Matías Menni. 2005. Reflective Kleisli subcategories of the category of Eilenberg-Moore algebras for factorization monads. Theory and Applications of Categories [electronic only] 15 (2005), 40–65. http://eudml.org/ doc/125160

Replies (3)

@ohad@mathstodon.xyz 2026-04-29 17:52

@maxsnew You can also derive it from descent data, but I think that's more complicated and I have a substantial technical debt to unpack there.

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@maxsnew@types.pl 2026-04-29 18:05

@ohad I'd be surprised if there's no earlier reference. There's a cool way to view Yoneda/CoYoneda in these terms btw that I think I've posted here before. CoYoneda says that every presheaf is a canonical quotient of a free algebra, and Yoneda says that every presheaf is a canonical sub-coalgebra of a cofree coalgebra.

Open ##2044532
@varkor@mathstodon.xyz 2026-04-29 22:33

@ohad The result is far older than that. For instance, the 2-dimensional version already appears in §6.6 of Blackwell–Kelly–Power's 1989 "Two-dimensional monad theory". I don't know what the oldest reference is, but I would imagine it's been known since the 1960s.

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