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

()():ZMfldn×Algnaug(V)V. \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 AAlgnaug(V)A \in \mathrm{Alg}_ n^{\mathrm{aug}}(\mathcal{V}) and consider this a functor ()A:ZMfldnV\int _{(-)}A\colon \mathrm{ZMfld}_ n \to \mathcal{V}. We can then prove theorems such as \otimes -excision. As far as categories go, ZMfldn\mathrm{ZMfld}_ n is not the best category to apply category-theoretic techniques to. In this talk, we will fix an MZMfldnM_* \in \mathrm{ZMfld}_ n and consider the functor

M():Algnaug(V)V. \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 nn-disk algebras and zero-pointed manifolds.