universal property of Ind kappa
Proposition
Let \(\kappa\) be a regular cardinal, \(\mathcal{C}\) a small infinity category and \(\mathrm{Ind}_{\kappa}(\mathcal{C})\) the infinity category Ind kappa.
Then for each \(\infty\)-category \(\mathcal{D}\) which admits \(\kappa\)-filtered colimits, there exists an joyal equivalence between
where \(\mathrm{Fun}^{\kappa}(-,-)\) is the full infinity subcategory containing infinity functors which preserve kappa filtered colimits
Proof
FW: 6.61 c)