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This question (as the title obviously suggests) is similar to, or a continuation of, this question that was asked years ago on MO by a different user. The present question, though, is different from ...

I've begun to interest in algebraic theories and their categorical models: in particular monads, generalized multicategories and operads, lawvere theories and their generalization. Is there any ...

TL;DR. Many cohomologies can be unified using comonads. Question: which cohomologies cannot be? For each algebraic theory, there is an adjunction, and therefore a (co)monad (or called a (co)triple). ...

It's known that from every operad arises a cartesian monad whose algebras are the algebras for the operad. Leinster proved that there are different operads from which arise the same monad, in this way ...