On Uniqueness of ℙ-Twists

Abstract

\n We prove that for any $\\mathbb{P}^n$-functor all the convolutions (double cones) of the three-term complex $FHR \\xrightarrow{\\psi } FR \\xrightarrow{{\\operatorname{{\\epsilon }}}} {\\operatorname{Id}}$ defining its $\\mathbb{P}$-twist are isomorphic. We also introduce a new notion of a non-split $\\mathbb{P}^n$-functor.