Categorical Nonstandard Analysis

In the present paper, we propose a new axiomatic approach to nonstandard analysis and its application general theory of spatial structures in terms category theory. Our framework is based on idea internal set theory, while make use an endofunctor U topos sets S together with natural transformation υ, instead as “standard”, “internal”, or “external”. Moreover, notion space called U-space, USpace whose objects are U-spaces morphisms functions U-spatial morphisms. The USpace, which shown be Cartesian closed, gives unified viewpoint toward topological coarse geometric structure. It will also useful further study symmetries/asymmetries systems infinite degrees freedom, such quantum fields.