Timeline for Algebraically-free monadicity theorem

6 events

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Jan 25 at 22:04	comment	added	David White		Sorry for the minor edit. I'd accidentally downvoted when I'd meant to upvote, but with a recent edit one can change that.
Jan 25 at 22:03	history	edited	David White	CC BY-SA 4.0	Fixed a minor thing, retagged
Mar 26, 2022 at 13:30	comment	added	varkor		@VladimirSotirov: that's an interesting observation, thanks! (Presumably this is something you spotted and isn't written down in the literature anywhere?)
Mar 25, 2022 at 23:56	comment	added	Vladimir Sotirov		Perhaps related: monadicity still holds if you drop the right unit axiom $\mu\circ T\eta=\mathrm{id}$ from the monad axioms but keep the same notion of algebras. The resulting forgetful functors $u$ are characterized by creating $u$-split coequalizers and there being a factorization $\mu=u\epsilon f$ for $\epsilon:fu\to\mathrm{id}$ such that the right triangle identity $u\epsilon\circ\eta u=\mathrm{id}_u$ holds. Usual monadicity follows from an equivalence of the left triangle identity $\epsilon f\circ f\eta=\mathrm{id}_f$ and the right unit axiom (because such $u$ are faithful as usual).
Mar 22, 2022 at 21:22	answer	added	aws		timeline score: 3
Mar 21, 2022 at 20:02	history	asked	varkor	CC BY-SA 4.0