On uniqueness of P-twists

Abstract

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

v5: 18 pages, minor revisions throughout