The arbitrary-characteristic Morita equivalence conjecture

Let $\Bbbk$ be a field, let the Morita equivalence in Theorem~ be the equivalence associated with the cyclotomic web construction, and let the Morita equivalence in Theorem~ be the equivalence between the $W$-Schur and web categories. The arbitrary-characteristic Morita equivalence conjecture. The Morita equivalence in Theorem~ and the Morita equivalence in Theorem~ remain valid over any field $\Bbbk$ of arbitrary characteristic. This proposes characteristic-independent extensions of the two stated Morita equivalences; the supplied text gives no resolution status.