\ \G,\ \F}$$ and some others [@MR]. For this instead of four-dimensional arithmetical space $\R^4$, adopted in sets theory, the role of the world of events passes to its “analogue” $$R^4=\ell C^{\infty}(\R^4)\in {\bf Set^{L^{op}} },$$ where ${\bf L}$ is the category of loci, i.e. the opposite category of finitely genereted $C^{\infty}$-smooth rings. Every its object $\ell A$ is a $C^{\infty}$-smooth ring which has the form $\ell A=\ell C^{\infty}(\R^n)/I$, where $I\subset C^{\infty}(\R^n)$ is an ideal and symbol $\ell$ is the label of opposite object. The category ${\bf L}$ contains the usual category ${\bf M}$ of $C^{\infty}$-manifolds: $${\bf M}\subset
{\bf L} \subset {\bf Sh( L)}
    \subset {\bf Set^{L^{op}} }$$ A morphism or arrow in ${\bf L}$ requires more the explicit description:

If $B=C^{\infty}(\R^n)/J$,  $A=C^{\infty}(\R^m)/I$, a morphism $\ell B\to \ell A$ is an equivalence class of smooth function $\phi:\R^n \to \R^m$ with property that $f\in I \Rightarrow f\circ\phi\in J$, while $\phi$ is equivalent to $\phi^\prime$ if componentwise, $\phi_i-\phi^\prime_i \in J \ (i=1,...,m).$

Our viewpoint will be to regard ${\bf Set^{L^{op}} }$ as a generalized set-theoretic universe, where – intuitively – every set is a smooth space (and the old Cantor sets are embeded as discrete spaces).

An event $x$ as [*an element in 