Reedy categories form a generalization of the category of finite ordinals, with morphisms the weakly monotone functions between them. Given a Reedy category C and a Quillen model category M, there is always a model structure on the category of functors from C to M. In this talk, we study Reedy categories which are enriched over a field and we present two main results. The first is an analogue of the aforementioned result for complete cotorsion pairs and abelian model structures. In the second result, we focus on linear Reedy categories having finitely many objects, which leads us to the concept of Reedy finite-dimensional algebras. We prove that any Reedy finite-dimensional algebra is quasi-hereditary with an exact Borel subalgebra. This is joint work with Jan Stovicek.

All algebras and modules in this talk are finite dimensional over a field. A module M is non-trivially decomposable if and only there exists an endomorphism f of M such that the characteristic polynomial of f has at least two different irreducible factors. Hence, all endomorphisms of an indecomposable module has a characteristic polynomial a power of an irreducible polynomial. The talk will discuss these observations and which irreducible polynomials occur when over a finite prime field. This is work in progress and based on joint work with Fernando Yamauti.