Some categorical aspects of the inverse limits in ditopological context

[摘要] This paper considers some various categorical aspects of the inverse systems (projective spectrums) and inverse limits described in the category if PDitop , whose objects are ditopological plain texture spaces and morphisms are bicontinuous point functions satisfying a compatibility condition between those spaces. In this context, the categoryInv ifPDitop consisting of the inverse systems constructed by the objects and morphisms of if PDitop , besides the inverse systems of mappings, described between inverse systems, is introduced, and the related ideas are studied in a categorical - functorial setting. In conclusion, an identity natural transformation is obtained in the context of inverse systems - limits constructed in if PDitopand the ditopological infinite products are characterized by the finite products via inverse limits.

[学科分类] 几何与拓扑

[关键词] inverse limit;natural transformation;co-adjoint functor;ditopology;concrete isomorphism;joint topology