Definition 22.1.1. Let \(\Kk \) be a collection of small \(\infty \)-categories and let \(C\) be a small \(\infty \)-category. We denote by \[ \PSh ^{\Kk }(C) \subseteq \PSh (C) \] the smallest full subcategory of \(\PSh (C)\) that contains the representable presheaves and is closed under \(I\)-indexed colimits for all \(I \in \Kk \).
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