Hello John,
I make references to Topos theory, largely with connection to the algebraic or projective varieties with Zariski topology. This is the basis of what might be called "pre-topos" theory. It is a form of pre-sheaf construction, which can be used to build a sheaf theory. One main interest is in a twistor geometry with E_6 subroup (or E_6xE_8) with a sheaf or pre-sheaf construction for twistor geometry.
There is a relationship between lightcones and Heisenberg groups within this Kleinian quotient system. I tend to see this as a precursor for the far more generalized system you present in your paper. I am also interested in the prospect for monster-moonshine structure, which is are projective varieties in 26 dimensions (eg the bosonic string) with Lorentzian structure. These projective varieties form the pre-sheaf construction for topos or grothendieck-Etale structure.
The space of lightlike geodesics is a set of invariants and then due to a stabilizer on O(n,2), so the space of lightlike curves L_n is identified with the quotient O(n,2)/P, where P is a subgroup defined the quotient between a subgroup with a Zariski topology, or a Borel subgroup, and the main group G = O(n,2). This quotient G/P is a projective algebraic variety, or flag manifold and P is a parabolic subgroup. The natural embedding of a group H - -> G composed with the projective variety G - ->G/P is an isomorphism between the H and G/P. This is then a semi-direct product G = P x| H. For the G any GL(n) the parabolic group is a subgroup of upper triangular matrices. An example of such a matrix with real valued elements is the Heisenberg group of 3x3 matrices (sorry for the inconvenient representation, but I have bad luck with these html-TeX systems)
|1 & a & b|
|0 & 1 & c|
|0 & 0 & 1|
which may be extended to n-dimensional systems to form the 2n+1 dimensional Heisenberg group H_n of n + 2 entries
|1 & a & b|
|0 & I_n & c|
|0 & 0 & 1|
where for O(n,2) the Heisenberg group is H_{2n+3}. The elements a and c are then n+2 dimensional row and column vectors of O(n,2). These are Borel groups, which emerge from the quotient space AdS_n/Γ, where the discrete group Γ is a manifestation of the Calabi-Yau 3-cycle, and which as it turns out gives an integer partition for the set of quantum states in the AdS spacetime. So both spacetime and quantum structure as we know them are emergent.
This of course can exist in more general setting, which is the type of construction you are presenting with the continuum hypothesis. I will not write that with alephs, for the Unicode representation does not work well. This suggests that the universe (the system of multi-cosmologies or multiverse) has this underlying system of topos between different structures. The system above illustrates how lightcones and Heisenberg groups emerge from the same quotient structure, where the topology indicates this is a form of topoi.
Cheers LC