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Thread quivers

This is a work in progress with C. Paquette and J.D. Rock. Starting from a directed graph Q, which we call a "quiver", we construct a new one Q' called "thread quiver" by replacing arrows with linearly ordered posets. Then we consider a k-linear category C where objects are the union of vertices of Q and elements of linearly ordered posets, and morphisms are given by 'paths'. We study pointwise finite representations of C or quotients of C by weakly admissible ideals. Our main interest is to study the decomposition of pointwise finite representations and homological properties of such categories.