0N47 Lemma 3.18. For π±\mathcal{V} a symmetric monoidal β\oo-category which is β\otimes-presentable, factorization homology valued in π±\mathcal{V} satisfies β\otimes-excision: for any πβπππππ‘\disk_{n}^{B}-algebra AA in π±\mathcal{V}, and for any collar-gluing Mβ²ββM0ΓββMβ²β²β MM^{\prime}\underset{M_{0}\times\mathbb{R}}{\bigcup}M^{\prime\prime}\cong M among BB-framed nn-manifolds, the canonical morphism in π±\mathcal{V} β«Mβ²Aββ¨β«M0ΓβAβ«Mβ²β²Aβββ«MA\int_{M^{\prime}}A\bigotimes_{\displaystyle\int_{M_{0}\times\mathbb{R}}A}\int_{M^{\prime\prime}}A\xrightarrow{~\simeq~}\int_{M}A is an equivalence.