This is a long document. I don’t see at the start something which
encapsulates the topic. Homotopy Type Theory (HoTT). HoTT is based on
homotopy, which is a system of diffeomorphisms on sub-space regions of a
manifold that describe invariants based on obstructions. These denoted as
π_p(M^n) = 0, ℤ or ℤ_i. for i an integer. The first fundamental form is
π_1(M^n), or a set of curves that are equivalent under diffeomorphisms.
These are related to homology groups H_p(M^n), but with additional
commutator information.
Physics with partition functions or path integrals
Z[φ] = ∫δ[φ]e^{-iS[φ]}
For the integration measure δ[φ] = d^nx/diffeo[φ]. The continuous maps or
diffeomorphisms are in a sense lifted away from what is fundamental, being
a form of coordinate or gauge condition. What is left is then analogous to
what is computed by a topological charge.
I am not sure if these document or others lead to this prospect, but if it
did it would be of considerable interest. If the binary on or off
definition of HoTT were connected to physics this way it would be of
interests. In particular if this connected with entanglements it would also
be of interest.
LC
On Friday, August 14, 2020 at 1:34:55 AM UTC-5 [email protected] wrote:
> Inroduction to Univalent Foundations of Mathematics with Agda
> 4th March 2019, version of 13 August 2020
>
>
> https://www.cs.bham.ac.uk/~mhe/HoTT-UF-in-Agda-Lecture-Notes/HoTT-UF-Agda.html
>
> @philipthrift
>
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