The universal continuous six functor formalism on light condensed anima
Li He
TL;DR
This paper generalizes the universal property of the six-functor formalism from locally compact Hausdorff spaces to light condensed spaces by establishing that $\mathrm{Shv}( - ;\mathrm{Sp})$ is initial among all six-functor formalisms on $\mathrm{Corr}(\mathrm{CondAn}^{\mathrm{light}},E)$ subject to mild dualizability, conservativity, and limit-preservation conditions. Building on Heyer–Mann's extension framework, the authors extend Zhu's initiality to the condensed setting via a canonical morphism $\alpha: \mathrm{Shv}( - ;\mathrm{Sp})\to D(-)$ and prove that $\alpha$ respects suave/prim adjunctions, yielding alignment between the ProFin^light and CondAn^light formalisms. As applications, they show that pullbacks along projections to intervals (e.g., $X\times \mathbb{R}$) are fully faithful for any such formalism, demonstrating interval-stability and descent-compatible behavior. Overall, the work provides a canonical, universal six-functor framework for light condensed spaces with implications for duality, descent, and functorial comparison across condensed geometric contexts.
Abstract
After the universal property of the six functor formalism $\Shv(-;\Sp)$ on locally compact Hausdorff spaces given by Zhu, we show that the six functor formalism $\Shv(-;\Sp)$ on light condensed anima in the sense of Heyer-Mann is initial among all six functor formalisms $D$ satisfying some mild conditions, and then we present some applications.