The paracyclic stable infinity-category and connective spherical complex correspondence

An infinity-category of paracyclic stable infinity-categories is understood as the category whose objects are paracyclic stable infinity-categories, and an infinity-category of connective spherical complexes of stable infinity-categories is understood as the category whose objects are connective spherical complexes of stable infinity-categories.

Paracyclic–spherical correspondence. There is an equivalence of infinity-categories between the infinity-category of paracyclic stable infinity-categories and the infinity-category of connective spherical complexes of stable infinity-categories.

This is proposed as a result of further study of the categorified Dwyer–Kan correspondence and its restriction to cyclic structures; the source says that this work is in progress, so the assertion remains open.