Torsor rewrites

With the notation conventions from em-convex, there are 3 pairs of torsor rewrites.  A torsor, figured by a fat circle here, is a term T of type  T: E \rightarrow E \rightarrow E \rightarrow E

with the rewrites:

t1

and

t2

Finally, there is a third pair of rewrites which involve terms of the form \circ A for A: N

t3

The rewrite T3-1 tells that the torsor is a propagator for \circ A, the rewrite T3-2 is an apparently weird form of a DIST rewrite.

Now, the following happen:

  • if you add the torsor rewrites to em-convex then you get a theory of topological groups which have a usual, commutative smooth structure, such that the numbers from em-convex give the structure of 1-parameter groups
  • if you add the torsor rewrites to em, but without the convex rewrite then you get a more general theory, which is not based on 1-parameter groups,  because the numbers from em-convex give a structure more general
  • if you look at the emergent structure from em without convex, then you can define torsor terms whch satisfy the axioms, but of course there is no em-convex axiom.

Lots of fun, this will be explained in em-torsor soon.

 

 

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