Resolutions in factorization categories
  Generalizing Eisenbud's matrix factorizations, we define factorization categories. Following work of Positselski, we define their associated derived categories. We construct specific resolutions of factorizations built from a choice of resolutions of their components. We use these resolutions to lift fully-faithfulness statements from derived categories of Abelian categories to derived categories of factorizations and to construct a spectral sequence computing the morphism spaces in the derived categories of factorizations from Ext-groups of their components in the underlying Abelian category. 
Matthew Ballard, Dragos Deliu, David Favero, M. Umut Isik, Ludmil   Katzarkov
math.CT math.AC math.AG