Category theory: assumes compositionality of morphisms ... which is essentially computational reducibility.
Insofar as category theory models mathematics, that is why mathematics avoids irreducibility.
What is “complexity-based category theory”?
Building up to rulial space
Progressively higher-order morphisms limit to rulial space, in which arrows are inevitably reversible; hence it is a topos
Possible claim: the reconstructed “space space” in rulial space is like the homotopy type
But the branchial structure is like the infinity topos (?)
Grothendieck hypothesis is basically the statement that branchial space is a space...
[Grothendieck hypothesis: why FTL is hard]
GH : true because of comp. irreduc.
When you do higher-order morphisms ... you’re reaching the PCE level
Either: everything is trivial, and then you can’t get anywhere in the higher-order morphisms .... or eventually you reach the PCE level
Do all non-small categories reach PCE? [Ramseyesque?]
E.g. morphism is successor
Foliation of multiway graph
Computational boundedness of the foliation process:
related to geometry/finite dimensionality
There exists a non-Groth. foliation of branchial space, but to find it is not computationally bounded
Existence of foliations in physics is required for a “state evolving” “mechanistic” model of physics
Strong hyperbolicity implies foliatability;
well-posedness : can make it an initial value problem
Existence of foliations in metamathematics
Hilbert’s program is well-posedness of math
In the theorem
theorem interpretation of MW graph...
there is a meaningful current global state of math
Cohesiveness of math??
Is there forward progress where all time vectors point to the future?
[Continuity to hypersurface is what prevents random “forward” vectors from pointing backwards]