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Let $ \mathcal{K}$ be a $ \lambda$ -accessible category and $ \hat{\mathcal{K}}$ its free completion under connected limits. Is $ \hat{\mathcal{K}}$ still accessible? $ \mathcal{K}$ can be identified with a subcategory of $ \text{Set}^{\text{Pres}_{\lambda}(\mathcal{K}) ^{\text{op}}}$ , is it true that $ \hat{\mathcal{K}}$ is just the closure under connected limits of this subcategory? It looks likeRead more