Representation theoretic aspects of Reedy categories

Natural numbers and the weakly monotone functions between them form a category Δ, which is fundamental in the theory of simplicial sets. Reedy categories were introduced for the purposes of homotopy theory as a generalisation of Δ. In this talk, we consider Reedy categories having finitely many objects and their linearisations. These correspond to certain finite dimensional algebras, that we call Reedy algebras. We will explain representation theoretic properties of Reedy algebras, based on joint works with J. Stovicek, and with T. Conde and S. Koenig.