In joint work with Georgios Dalezios, we studied a K-linear analogy of the classical notion of Reedy category over a field K. Examples of such K-linear categories which are Hom-finite and with finitely many objects can be in a usual way encoded by finite dimensional algebras, which we call Reedy algebras. On one hand, we focused on representation theoretic properties of linear Reedy categories and especially Reedy algebras. In view of a recent result of Conde, Dalezios and Koenig, it turns out that Reedy algebras are precisely quasi-hereditary algebras with a so-called triangular decomposition. On the other hand, the raison d'être of ordinary Reedy categories is that model category structures lift to categories of diagrams of Reedy shapes, and we proved an analogous result about lifting cotorsion pairs to functor categories from linear Reedy categories.