What's the name of this mathematical structure

Stream: new members

[Kevin Sullivan]

Dear all:

Suppose I have an affine space, S. On that space I have a set , F, of all possible coordinate systems (each induced by a different affine frame). Between each ordered pair, (f1, f2), of coordinate systems in F we have a change-of-coordinates isomorphism, i_f1_f2. Let I_S denote the set of all such isomorphisms between all affine coordinate systems on F. What's the right abstract algebraic name for the algebraic structure, I_S?

[Yaël Dillies]

docs#affine_equiv, maybe?

[Kevin Sullivan]

Yaël Dillies said:

docs#affine_equiv, maybe?

Yes, that's the type in mathlib of a pair of transforms between any two coordinate systems. I'm looking for the abstract algebraic name of the set of all such isomorphisms on the set of all possible affine coordinate systems.

[Bart Michels]

Do you mean https://en.wikipedia.org/wiki/Affine_group ?

[Kevin Sullivan]

Thank you. That's close but not quite it. That concept involves mappings of a space to itself. What we've got in my case are (1) a base affine space, S; (2) a set of affine coordinate spaces, F (where each associates a coordinate tuple with each point and vector in S and where these coordinate tuples are the points and vectors of the new affine coordinate space); and where we're now looking at the set of all isomorphisms between these affine coordinate spaces.

[Reid Barton]

A groupoid?

[Kevin Sullivan]

Reid, yes, this seems to be right. Thank you.

[Kevin Sullivan]

I should have remembered that!