I'm looking at the proof of Higher Algebra Proposition 6.1.6.27, and in the very first sentence of the proof, Lurie states:
The functor $(F\delta)_{\Sigma_n}$ is n-homogeneous by Proposition 6.1.5.4.
Checking back to 6.1.5.4, I see the statement
Let $C$ be a small $\infty$-category which admits finite colimits and let $D$ be an $\infty$-category which admits finite limits and small filtered colimits. Assume that filtered colimits in $D$ are left exact. Then composition with the Yoneda embedding $j : C \to Ind(C)$ induces a fully faithful
functor $$\theta : Exc^n_c (Ind(C),D)) \to Fun(C,D)$$
whose essential image is the full subcategory $Exc^n(C,D) \subset Fun(C,D)$ spanned by the n-excisive functors.
which seems totally irrelevant.
Does anyone know what the correct reference is, or if the reference is correct, how to apply the proposition to achieve the result?
Best Answer
The correct reference is 6.1.4.14. (And the hypothesis of 6.1.6.27 should refer to countable limits and colimits, rather than finite limits and colimits.)