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### What kind of operations does the Tall-Wraith monoid encode?

According to the nLab page, for an algebraic theory V a Tall–Wraith V-monoid is "the kind of thing that acts on V-algebras". Well, it certainly does act on V-algebras, but in which sense is it "the ...

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### How exactly is Hochschild homology a monad homology?

Many texts which praise the generality of the bar construction associated to a monad, say that Hochschild homology is an example of this.
What exactly is in this case the underlying endofunctor of ...