In a recent paper by Green, Psaroudakis and Solberg the authors recover old and show new reduction techniques for the finitistic dimension conjecture. The finitistic dimension fin.dim(A) of a finite dimensional (or, more generally, Artin) algebra A is the supremum of the projective dimensions of the finitely generated A-modules with finite such dimension. The conjecture states that fin.dim(A) is finite, for any such algebra A. Auslander and Reiten showed that a sufficient condition for fin.dim(A) to be finite is that the subcategory