Let $\mathcal{V}$ be a symmetric monoidal stable $\infty$-category, satisfying appropriate adjectives. (Reduced) factorization homology is then a functor

$\int _{(-)} (-)\colon \mathrm{ZMfld}_n \times \mathrm{Alg}_n^{\mathrm{aug}}(\mathcal{V})\to \mathcal{V}.$

The way we have viewed this so far is to fix an $A \in \mathrm{Alg}_n^{\mathrm{aug}}(\mathcal{V})$ and consider this a functor $\int _{(-)}A\colon \mathrm{ZMfld}_n \to \mathcal{V}$. We can then prove theorems such as $\otimes$-excision. As far as categories go, $\mathrm{ZMfld}_n$ is not the best category to apply category-theoretic techniques to. In this talk, we will fix an $M_* \in \mathrm{ZMfld}_n$ and consider the functor

$\int _{M_*}(-)\colon \mathrm{Alg}_n^{\mathrm{aug}}(\mathcal{V})\to \mathcal{V}.$

The only explicit calculation we know about this functor is its values on free algebras, which we did in the case of (non-zero-pointed framed) manifolds in the first talk. We shall begin by setting up the analogous version for augmented $n$-disk algebras and zero-pointed manifolds.