In this paper, inverse systems (spectrums) and their inverse limits are described and investigated in the some special subcategories of the category whose objects are ditopological texture spaces and morphisms are the point functions satisfying a compatibility condition, besides bicontinuity. According to that, we especially restrict ourselves to the topological subcategory ifPDitop consisting of point functions as above and ditopological spaces that have plain texturing which is proper, but still quite extensive subclass of texturings. Followed by, so many major properties of inverse systems and limits in the context of category ifPDitop are constructed under the most general conditions. In particular, by considering the full subcategory ifPDicomp of ifPDitop, whose objects are dicompact plain spaces, we acquired various results about the theory of inverse systems consisting of dicompact plain spaces. (C) 2017 Elsevier B.V. All rights reserved.