such that $ \psi \circ f \notin  \Gamma $.

3\) If $f \in  {\rm Hom}_{\E}(a,R_{T}) \setminus \Psi $ then there exists $\phi  \in  \Phi $ such that $ f\circ \phi  \notin  \Gamma$.

4\) For any monomorphisms $f:\Omega \mapsto a , g:\Omega \mapsto R_{T}$ there exists $\phi  \in  \Phi $ such that $\phi \circ g = f$.

5\) For any monomorphisms $f:\Omega \mapsto a, g :\Omega \mapsto R_{T}$ there exists $\psi  \in  \Psi $ such that $\psi \circ f = g $.

Here $\Omega$ is the subobject classifier in $\E$.

An affine object in category ${\bf Set}$ is the set equipped with an affine structure [@Io]. In the topos ${\bf Bn}(M)$ and in the spatial topos $ {\bf Top}(M)$ (see notations in [@Go]), an affine object is a fiber bundle with base $M$ and affines space as fibers.

A categorical description of the Relativity means the introduction of the Lorentz structure either in an affine space or in a fiber bundle with affine spaces as fibers. This can be done by defining in the affine space a family of equal and parallel elliptic cones or a relativistic elliptic conal order [@AGS].

Below we shall use the notations from [@Go].

Let $ 