Proposition 22.3.6 ([Lurie (2009), Corollary 4.2.3.11, Propositions 5.3.2.9, 5.3.5.10 and 5.3.5.14, and Theorem 5.5.1.1]). If \(C\) is a small \(\infty \)-category with finite colimits, then \(\Ind (C)\) admits small colimits and is presentable. Moreover, the inclusion \(C\hookrightarrow \Ind (C)\) preserves finite colimits, and the inclusion \[ \Ind (C)\hookrightarrow \PSh (C) \] identifies \(\Ind (C)\) with the full subcategory spanned by the presheaves \(C\catop \to \An \) which send finite colimits in \(C\) to limits in \(\An \).
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