Torsor

A G 𝐺 G -torsor for a Group G 𝐺 G is a Group Action α : G × T → T : 𝛼 → 𝐺 𝑇 𝑇 \alpha:G\times T\to T on an Merely Inhabited H-Set T 𝑇 T such that the Shear Map ⟨ α , π 2 ⟩ : G × T → T × T : 𝛼 subscript 𝜋 2 → 𝐺 𝑇 𝑇 𝑇 \langle\alpha,\pi_{2}\rangle:G\times T\to T\times T is an Isomorphism.

Note that we can drop the requirement that T 𝑇 T be nonempty to obtain the notion of a Pseudo-Torsor.

Single-Sorted Definition

Torsors are equivalent to Merely Inhabited Grouds.