Generalized negligible morphisms and their tensor ideals

Abstract We introduce a generalization of the notion negligible morphism and study associated tensor ideals thick ideals. These are defined by considering deformations given monoidal category $${\mathcal {C}}$$ C over local ring R . If maximal ideal is generated single element, we show that any admits an explicitly modified trace function. As examples consider various Deligne categories tilting modules for quantum group at root unity semisimple, simply connected algebraic in prime characteristic. prove elementary geometric description type A propose similar one modular case.