Almost Split Sequences and Representations of Finite Posets

The theory of Rep(k, S), the category of finite-dimensional representations of a finite poset S over a field k, is applicable to both finite rank Butler groups [Ar] and [AD] and finite valuated groups [ARiV], Elements of Rep(k, S) are denoted by U = (U,U(s)|s∈S), where U is a finite dimensional k-vector space, each U(s) is a subspace of U, and if s ≤ t in S, then U(s) is contained in U(t).