  We construct a nerve functor parametrized by a choice of quantale, exhibiting
both the Vietoris-Rips complex and the magnitude nerve as instances of this
nerve for different choices of monoidal structure on $\mathbb{R}$. Furthermore,
the difference between how persistent homology processes the Vietoris-Rips
complex and how magnitude homology processes the magnitude nerve is cast as a
choice of whether or not to "localize" the corresponding nerves along
$\mathbb{R}$ in a precise sense. Lastly, we mention some application-oriented
observations naturally suggested by the perspective mentioned above.
