  We generalize our previous lattice construction of the abelian bosonization
duality in $2+1$ dimensions to the entire web of dualities as well as the
$N_f=2$ self-duality, via the lattice implementation of a set of modular
transformations in the theory space. The microscopic construction provides
explicit operator mappings, and allows the manifestation of some hidden
symmetries. It also exposes certain caveats and implicit assumptions beneath
the usual application of the modular transformations to generate the web of
dualities. Finally, we make brief comments on the non-relativistic limit of the
dualities.
