Abstract
Using the framework of ambidexterity developed by Hopkins and Lurie, we introduce a parametrized analogue of higher semiadditivity called $\mathcal Q$-semiadditivity, depending on a chosen class of morphisms $\mathcal Q$. Our first main result identifies the free $\mathcal Q$-semiadditive parametrized category on a single generator with a certain parametrized span
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