  We provide sharp cylindrical parametrizations of cylindrical cell
decompositions by maps with bounded $C^{r}$ norm in the sharply o-minimal
setting, thus generalizing and strengthening the Yomdin-Gromov Algebraic Lemma.
We introduce forts, geometrical objects encoding the combinatorial structure of
cylindrical cell decompositions in o-minimal geometry. Cylindical
decompositions, refinements of such decompositions, and cylindrical
parametrizations of such decomposition become morphisms in the category of
forts. We formulate and prove the above results in the language of forts.
