  We use the abstract setting of excisive functors in the language of
$\infty$-categories to show that the best approximation to the
$\ell^1$-homology functor by an excisive functor is trivial.
  Then we make an effort to explain the used language on a conceptual level for
those who do not feel at home with $\infty$-categories, prove that the singular
chain complex functor is indeed excisive in the abstract sense, and show how
the latter leads to classical excision statements in the form of Mayer-Vietoris
sequences.
