space-time theory can exist physically different models; each topos gives us own physical world.

Application of topos theory in physics is one of the main intentions of the creator of this theory W.Lawvere [@La] The idea of using topoi for construction dynamically variable Universe belongs to russian philosopher I.A.Akchurin [@Ak]. The non-smooth topos theories of space-time was given in [@GT; @GD; @GOb]. The variants of smooth topos theory of space-time are explained in [@GJ; @GGC; @GO; @Gr; @GuI]. Application topos theory in quantum theory can be found in [@Tr; @Is].

Toposes and Foundation of Theory of Relativity
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The system of axioms for the Special theory of relativity contains fewer primery notions and relations, is simple, and lead directly to the ultimate goal (see review [@Gu]). In the case of the General relativity it is difficult to introduce a smoothness. This problem was studied by R.I.Pimenov (see in [@Pim] or presentation of result of [@Pim] in [@GOb]).

Does the unified way of axiomatization of these different physical theories exist? Does the unified way of axiomatization of these different physical theories exist? The language of topos theory [@Go; @Jo] gives the unified way of axiomatization of the Special and General Relativity, 