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The term I was looking for was affine structure, as I commented to someone else. But from your link, which I can't understand entirely, I get the sense that a t
by europeanguy 4y ago
The term I was looking for was affine structure, as I commented to someone else. But from your link, which I can't understand entirely, I get the sense that a torsor is an even bigger generalization.
- JadeNB 4y ago> The term I was looking for was affine structure, as I commented to someone else. But from your link, which I can't understand entirely, I get the sense that a torsor is an even bigger generalization. An affine space is a torsor under a vector space, and you can have instead a torsor under any group. This loses a bit of structure, in the sense that you can take convex combinations in an affine space but not in an arbitrary torsor; but otherwise it is a proper generalisation. But the convex combination $(a + b)/2$ used to obtain a midpoint is exactly what we want here!