With Yoann Dabrowksi.

The study of Differential Linear Logic argues for models of Linear Logic where proofs are interpreted as smooth functions between vector spaces endowed with a topology. However, several difficulties appears in this context : it is not trivial to endow a tensor product with a good topology, nor to find a cartesian closed category of smooth maps, or to construct a star-autonomous category of topological vector spaces. We argue that the construction of these models should be done from the "parr" perspective, by interpreting this connective as the well-known epsilon product of Schwartz. We exhibit several smooth classical models of Linear Logic, and argue for a general setting for the construction of such models.