Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
for completeness, with pointer to
added pointer to:
added Grothendieck’s alternative “formally principal homogeneous space”
Also added pointer to pages 73-74 in
added pointer to
which already has the term “formally principal” on p. 15 (without the “homogeneous”)
So I guess the category of pseudotorsors for G is (equivalent to) the result of adding a formal initial object to the groupoid BG?
It’s that trivial only internal to Sets, but the point of the exercise is that it’s much more interesting when internalized in richer ambient categories. Such as schemes. Or G-spaces. Or G-schemes….
added one more source for the terminology “formally principal homogeneous”:
Alexander Grothendieck, p. 9 of Exemples et Complements (doi:10.1007/BFb0058666, pdf), which is p. 293 in:
Alexander Grothendieck, Michèle Raynaud, Revêtements étales et groupe fondamental (SGA 1), Lecture Notes in Mathematics 224, Springer 1971 (arXiv:math/0206203, doi:10.1007/BFb0058656)
cross-linked with empty heap
1 to 9 of 9