Projective Fraïssé limits and generalized Ważewski dendrites

We continue the study of projective Fraïssé limits of trees initiated by Charatonik and Roe and we construct many generalized Ważewski dendrites as the topological realization of a projective Fraïssé limit of families of finite trees with (weakly) coherent epimorphisms. Moreover we use the categorical approach to Fraïssé limits developed by Kubiś to construct all generalized Ważewski dendrites as topological realizations of Fraïssé limits of suitable categories of finite structures. As an application we recover a homogeneity result for countable dense sets of endpoints in generalized Ważewski dendrites.