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Patrik Eklund wrote:

In my view there is no logic monoid => monad...


It's pretty much been said, but I'll say it again:

We can generalize the concept of monoid from Set to any monoidal category
and then to any bicategory.  A monoid in Cat is then a monad.

Indeed, most people seem to call a "monoid" in a bicategory a "monad".

Best,
jb