  We construct combinatorial model category structures on the categories of
(marked) categories and (marked) pre-additive categories, and we characterize
(marked) additive categories as fibrant objects in a Bousfield localization of
pre-additive categories. These model category structures are used to present
the corresponding $\infty$-categories obtained by inverting equivalences. We
apply these results to explicitly calculate various limits and colimits in
these $\infty$-categories.
