A small #math thread about #barycenter, #torsor, and #extension.

A torsor for a group object (in a topos), or a principal homogeneous space under a group, or a principal bundle wrt a group (in differential geometry) are more or less the same thing: you are given a group G, an object P with a free and transitive action of G on P ((g,p)↦g⋅p) which tells you that P and G are very close: you have some p ∈ P, or you have such a p “locally”.

This is slightly complicated, I admit, but…