The uniqueness problem of dg-lifts and Fourier-Mukai kernels

Abstract

We address the uniqueness problem of dg-lifts of exact functors between triangulated categories, and its relationship with the uniqueness problem of Fourier-Mukai kernels. We prove a positive result under a vanishing hypothesis on the functors, employing A_infty-categorical techniques.

22 pages

References in corpus (2)

• Sur les A-infini catégories
• A-infinity functors and homotopy theory of dg-categories

Cited by in corpus (4)

• A tour about existence and uniqueness of dg enhancements and lifts
• The Homotopy Theory of $A_{\infty }$Categories
• Hochschild entropy and Categorical entropy
• A constructive approach to Fourier-Mukai transforms for projective spaces via $A_{\infty }$-functors between pretriangulated dg categories