The analytic–torsion orthogonal complement conjecture for FI-objects

Let $\FIVAnly$ be the $\infty$-category of analytic $\FI$-objects, and let $\FIVTors$ be the full sub-$\infty$-category of torsion $\FI$-objects. For full subcategories $\mathcal A$ and $\mathcal T$ of an $\infty$-category, write $\mathcal T^{\perp}$ for the right orthogonal complement of $\mathcal T$. Analytic–torsion orthogonal complement conjecture. The full sub-$\infty$-category $\FIVAnly$ is the right orthogonal complement of $\FIVTors$:

$$\FIVAnly=(\FIVTors)^{\perp}.$$

The preceding corollary shows that $\FIVAnly$ is contained in this right orthogonal complement; the conjecture asserts the converse inclusion, characterizing analytic $\FI$-objects as precisely those right-orthogonal to torsion objects.