Hello,

The thesis I'm working on is as follows:

1 / There is no change in the way of thinking since man lives in a group.
2 / To prove it, it is necessary to define what are the “thought patterns” of any Subject.
3 / The theory of categories can serve as a universal language model making it possible to identify these different patterns of thinking.
4 / This makes it possible to differentiate 3 levels of reflection, leading to

• The logic and elementary topos of Lawvere,

• A "topological approach", initiated by Évariste Galois and leading to Grothendieck's topos,

• A 3rd level where equivalences or "bridges" are established.

5 / This general scheme would make it possible to consider a "unitary" theory in physics.

I leave on my blog the traces of my own evolution in this program.
I try as I can, to discuss this subject within the Categorical Logic group led by Anatole Khelif at Paris Diderot.
Not being a mathematician at all, I try to find relays to improve my approach.

For a short summary of this approach : 
- En Français 
 - In English