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Jan 9, 2023 at 5:41 comment added Arshak Aivazian I'll accept this answer and a special thanks to everyone for your examples in the comments. It was very helpful for me.
Jan 9, 2023 at 5:41 vote accept Arshak Aivazian
Dec 24, 2022 at 18:13 comment added Tim Campion Maybe it's worth noting the following consequence of the Corollary: if $\mathcal C$ is already known to be monadic over $Set$, then in order to show that $\mathcal C$ is bimonadic, you need only check that $\mathcal C$ has an injective cogenerator.
Dec 24, 2022 at 17:57 history answered Tim Campion CC BY-SA 4.0