We introduce the notion of interlaced weak ditalgebras and apply reduction
procedures to their module categories to prove the tame-wild dichotomy for the
category F(Δ) of filtered by standard modules for a
quasi-hereditary algebra. Moreover, in the tame case, we show that given a
fixed dimension d, for every d-dimensional indecomposable module M∈F(Δ), with the only possible exception of those lying in a finite
number of isomorphism classes, the module M coincides with its
Auslander-Reiten translate in F(Δ). Our results are based on a
theorem by Koenig, K\"ulshammer, and Ovsienko relating F(Δ) with
the module category of some special type of ditalgebra.Comment: 51 page