0NNU Notation 8.2. From now on and until the end of section 9 we will work with a fixed infinite regular cardinal κ\kappa larger than ω\omega. We will denote by (Cat∞ex)κ(\Cat_{\infty}^{\ex})^{\kappa} the category of κ\kappa-compact small stable ∞\infty-categories (see §2.4).