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nLab > Latest Changes: transitive action

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2021

    added the definition in terms of the shear map being an epimorphism. Adjusted the discussion of requiring or not the underlying object to be inhabited.

    diff, v16, current

    • CommentRowNumber2.
    • CommentAuthoranon-a-moose
    • CommentTimeMay 12th 2024
    I'm confused why the shear map being an epimorphism is sufficient when looking at a transitive group action internal to a category. In some categories (such as Diff), epimorphisms are not necessarily surjections, but the transitivity definition would seem to imply that surjectivity is required.
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 12th 2024
    • (edited May 12th 2024)

    added the parenthetical remark that in more general ambient categories one may want to require stronger notions of epimorphisms (all of which will coincide in the base context of Sets that is considered in the previous paragraph).

    diff, v17, current

1 to 3 of 3

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