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The paper presents several quantum models constructed with the formalism ofalgebraic geometry. The Universe is presented as a presheaf on the "space ofultimation" (i.e. the branching future) with values in certain category whichenhances the category opposite to C*-algebras. Given models show thepossibility to derive ordinary space-times (of both Special and GeneralRelativity) from ultrametric spaces.

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