The presheaf of Quantum Realities and constructions of the space-time from the Space of Ultimation

The paper presents several quantum models constructed with the formalism of algebraic geometry. The Universe is presented as a presheaf on the “space of ultimation” (i.e. the branching future) with values in certain category which enhances the category opposite to C*-algebras. Given models show the possibility to derive ordinary space-times (of both Special and General Relativity) from ultrametric spaces.