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Sep 8, 2020 at 10:41 comment added Jiří Rosický It might be interesting o look at the old paper of J. Reiterman dml.cz/bitstream/handle/10338.dmlcz/106455/…
Sep 7, 2020 at 18:08 comment added varkor "I think there may not be much more to say at this level of generality" — it's also not clear to me. However, it doesn't seem unreasonable that there might be at least sufficient syntactic conditions that cover examples like the powerset monad and CHS monad. It is perhaps helpful to rephrase the condition that $T$ be varietal in these ways, but these reformulations are very direct, and it's not clear that there aren't stronger results at this level of generality.
Sep 7, 2020 at 17:16 history answered Tim Campion CC BY-SA 4.0