  We prove 2-categorical conservativity for any {0,T}-free fragment of MALL
over its corresponding intuitionistic version: that is, that the universal map
from a closed symmetric monoidal category to the *-autonomous category that it
freely generates is fully faithful, and similarly for other doctrines. This
implies that linear logics and graphical calculi for *-autonomous categories
can also be interpreted canonically in closed symmetric monoidal categories.
  In particular, every closed symmetric monoidal category can be fully embedded
in a *-autonomous category, preserving both tensor products and internal-homs.
In fact, we prove this directly first with a Yoneda-style embedding (an
enhanced "Hyland envelope" that can be regarded as a polycategorical form of
Day convolution), and deduce 2-conservativity afterwards from Hyland-Schalk
double gluing and a technique of Lafont. The same is true for other fragments
of *-autonomous structure, such as linear distributivity, and the embedding can
be enhanced to preserve any desired family of nonempty limits and colimits.
