Mateusz Baran

> We could introduce an Homogneous Space [wikipedia](https://en.wikipedia.org/wiki/Homogeneous_space) as a more generic case? This might be nice for some ManifoldDiffEq.jl solvers. I was thinking that again we have an abstract...

> Ok, then lets not include it in this PR. My idea is that some operations can already be defined on homogeneous spaces (and then inherited by Lie groups). So...

> Did I miss to move `GroupOperationAction`? I meant to exactly move all abstract stuff here. I don't see `GroupOperationAction` here. It's not abstract but I think it should be...

Hm, are you sure? `GroupOperationAction` doesn't store the action explicitly, and is not a manifold. Things like `RotationAction` or `TranslationAction` should be closer I think? Anyway, we may also introduce...

That's a good point -- the division between actions and their respective quotients is somewhat arbitrary and rearranging things a bit may be a good idea. > The current model...

It would be nice to improve the current design but it's a hard problem. Take `apply` as an example. It may need to know the manifold it acts on, the...

> I currently get confused that apply and an order rotates the order sometimes. And currently I am confusing Action and operation. Operation is internal to the group (a part...

> Sorry for all these posts – I really seem to miss a lot in the theory with actions operations and directions, sometimes actions seem operations (+ / *), then...

> So operation is matrix multiplication. > But if I have a manifold and a group, then still `a` from SO(3) and `p` from the manifold, then `a` is an...

> and this text does not include actions. So I must miss something. Is * the action? or g? It can not be g because g does not have a...