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user 156537
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Proof in Higher Algebra that $\mathcal{C}at(\mathcal{K})$ is presentable
In Higher Algebra Lemma 4.8.4.2, Lurie shows that for $\mathcal{K}$ a small set of simplicial sets, the $\infty$-category $\mathcal{C}at(\mathcal{K})$ of small $\infty$-categories with $K$-shaped coli …
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Proof in Higher Algebra that $\mathcal{C}at(\mathcal{K})$ is presentable
Note that by HTT 5.4.1.2 since $\tau$ is an uncountable regular cardinal, an $\infty$-category is $\tau$-compact iff it is $\tau$-small. Our first step is to show that the inclusion $\mathcal{C}at(\ma …
- 898