In Jordan Watt's thesis it is shown that Frölicher spaces form a full subcategory of diffeological spaces, so if the functor from Fréchet manifolds to diffeological spaces is fully faithful (as seems to be the case by the result of Losik), and if this functor factors through Frölicher spaces (as shown in Kriegl-Michor), then Frölicher spaces embed fully faithfully in Frölicher spaces.

In Jordan Watt's thesis it is shown that Frölicher spaces form a full subcategory of diffeological spaces, so if the functor from Fréchet manifolds to diffeological spaces is fully faithful (as seems to be the case by the result of Losik), and if this functor factors through Frölicher spaces (as shown in Kriegl-Michor), then Fréchet manifolds embed fully faithfully in Frölicher spaces.