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Confusion ! (in my head so help please). Quote from torsor:
“A left G-torsor over a group G is an inhabited object P equipped with a G-action, ρ:G×P→P etc. “
Am I dreaming or is there a problem with the wording? Note at group extension we find:
“For a group extension, we have that is an -torsor over ….”
If I understand correctly, the word ’over’ is being used in different ways. Perhaps in the first instance the ’over a group ’ is redundant. The torsor is in a general category at this point. In the second case the ‘over ’ refers to the fact that we are working in a slice category. Then the group involved is not but . Once I have clarified this I will alter the wording if necessary, but at the moment i find the uses less than clear.
The very first sentence had
A -torsor for a group…
I have changed both sentences now to
For a group, a -torsor is…
Thanks. The revised wording looks good.
I think it would be better something of the kind
“A torsor with structure group , or in short -torsor, is…”__
This may or may not (it is a bit redundant) be preceded by “Given a group ,”.
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