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    • CommentRowNumber1.
    • CommentAuthorGuest
    • CommentTimeMay 23rd 2023
    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeMay 23rd 2023

    You say the category is not the same as the category of abelian groups, which is true enough, but isn’t it equivalent to the category of pointed abelian groups, equivalently the undercategory or co-slice Ab\mathbb{Z} \downarrow Ab? “Pointed commutative invertible semigroup” just sounds so long-winded, if “pointed abelian group” would do. Do other people use this phrase?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 4th 2023

    There is (or maybe was) a trend of anonymous guests not reacting to substantial remarks on their edits (similarly here). I think we should wait maybe a couple more days but then go ahead and re-edit.

  1. I renamed this page to pointed abelian group, defining the object as an abelian group with an additional element, and I moved the definition as a “pointed commutative invertible semigroup” into a remark which states that the neutral element is not needed in the definition of pointed abelian group.

    Joachim Joszef

    diff, v2, current

  2. also added a link to pointed object in a monoidal category

    Joachim Joszef

    diff, v2, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJun 6th 2023
    • (edited Jun 6th 2023)


    I have expanded further and added more formatting.

    Also added a couple of references (fairly random ones, just to indicate that the concept is in use)

    diff, v3, current