+ P_0(\ell A)$$ for every $C^{\infty}$-smooth vector function $X(u)$.

It can hope that under some conditions which semigroup $P_0(\ell A)$ must be satisfied (for example, $P_0(\ell A)$ modulo $I$ is an elliptic cone) the order automorphisms are linear operators, which at the stage ${\bf 1}$ coinside with Lorentz transformations. In any case one appears the new circle of mathematical and physical problems concerning semigroup theory solving of which will be useful for given here approach to theory of space-time...

It is clearly possible to build a causal topos theory either by analogy with the content of Section 2, or by the scheme used in Sections 4, 5. However, the resulting space-time theory will be non-classical, different from that of the Minkowski space-time. This is a [*new*]{} theory of space-time, created in a purely logical manner. It will reflect the real space-time properties to the same extent as the development of mathematical abstractions accompanies the development of the real world.

Synthetic Theory of Relativity
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In his work W.Lawvere [@La] suggested a new approach to the differential geometry and to the others mathematical disciplines which are connected with physics. It allows to give the definitions of derivatives, tangent vectors and tangent 