> **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\\)?

Okay, I am totally wrong about this.

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).

Okay, I am totally wrong about this.

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).