Abstract We study distinguished objects in the category $\mathcal{B}\mathcal{L}$ of Banach lattices and lattice homomorphisms. The free construction introduced by de Pagter Wickstead [ 8] generates push-outs, combining this with an old result Kellerer 17] on marginal measures, amalgamation property is established. This will be key tool to prove that $L_1([0,1]^{\mathfrak{c}})$ separably $\mathc...

We discuss the following problem from the theory of regular incidence-polytopes. Given two regular d-incidence-polytopes 9X and !?2 such that the facets of 0>2 °d the vertex-figures of 0\ are isomorphic to some regular (d l)-incidence-polytope 3C, is there a regular (d +1)incidence-polytope X with facets of type ^ and vertex-figures of type &•?. Such amalgamations X of 0\ and 0*2 along 3iT exis...