I'm hoping to avoid having to prove by hand that a particular category is monadic, by a finitary monad, over another. It seems to me there should be a very general theorem that if one has an extension of essentially (many sorted) algebaric theories. then the category of models of the extension is monadic, by a finitary monad, over the category of models of the original theory. I'd be happy with some restrictions on the extension: the same set of sorts, no new equations imposed on the operations in the original theory, just new operations and equations on these. Does anyone have a citation for such a result? (Or one equivalent to it phrased in terms of sketches?) Such a result with additional hypotheses (which may or may not apply in my circumstance)? Or a result that obviously implies a result of the sort I want, but is stated in different terms? Best Thoughts, D.Y. You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/mail/deeplink/groupActions?source=EscalatedMessage&action=files&smtp=categories%40mq.edu.au&bO=true&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Leave group<https://outlook.office365.com/mail/deeplink/groupActions?source=EscalatedMessage&action=leave&smtp=categories%40mq.edu.au&bO=true&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>