??what about relationship between "(de-)categorified gram-schmidt matrix" and "euler form" ?? ...and so forth... ??some confusion here...

???something about resolution (and homology) vs filtration (and associated graded) ... ??...

??something about bilinear forms vs operators... ??bilinear forms arising from operators in combination with symmetric (or something...) bilinear forms ... ???something about "adjointness" ... ??

??something about "schur's lemma" vs non-semi-simple case ... ??? ...

so what _about_ filtration of indecomposable projective quiver representations by irreps, and resolution vice versa?? ...