On fully wild categories of representations of posets

Abstract

Assume that I is a finite partially ordered set and k is a field. We prove that if the category prin(kI) of prinjective modules over the incidence k-algebra kI of I is fully k-wild then the category fpr(I,k) of finite dimensional k-representations of I is also fully k-wild. A key argument is a construction of fully faithful exact endofunctors of the category of finite dimensional khx,yi-modules, with the image contained in certain subcategories.