> **Puzzle MD1**. If \$$M\$$ is a monad and \$$\mathrm{Lan}\_{M}\, I\_\mathcal{C}\$$ exists, then is it the case that \$$(\mathrm{Lan}\_{M}\, I\_\mathcal{C}) \circ M \cong M\$$?

Evidently if \$$M\$$ is a monad then \$$\mathrm{Lan}\_{M}\, I\_\mathcal{C}\$$, if it exists, is a *comonad*, according to [nLab's entry on adjoint's monads](https://ncatlab.org/nlab/show/adjoint+monad).