  To any rigid analytic space (in the sense of Fujiwara-Kato) we assign an
$\mathbb{A}^1$-invariant rigid analytic homotopy category with coefficients in
any presentable category. We show some functorial properties of this assignment
as a functor on the category of rigid analytic spaces. Moreover, we show that
there exists a full six functor formalism for the precomposition with the
analytification functor by evoking Ayoub's thesis. As an application, we
identify connective analytic K-theory in the unstable homotopy category with
both $\mathbb{Z}\times\mathrm{BGL}$ and the analytification of connective
algebraic K-theory. As a consequence, we get a representability statement for
coefficients in light condensed spectra.
