# 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:

and

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

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.