Movability of Morphisms in an Enriched Pro-Category and in a $$\boldsymbol{J}$$ -Shape Category

Abstract

Various types of movability for abstract classical pro-morphisms or coherent mappings, and for abstract classical or strong shape morphisms was given by the same authors in some previous paper [10–12]. In the present paper we introduce and study the notions of (uniform) movability, and (uniform) co-movability for a new type of pro-morphisms and shape morphisms belonging to the so called enriched pro-category \(pro^{J}\)-\(\mathcal{C}\) and to the corresponding shape category \(Sh^{J}_{(\mathcal{C},\mathcal{D})}\), which were introduced by Uglešić [27].