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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 3rd 2020

    copied over, from overcategory, statement and proof of computing limits in undercategories

    diff, v16, current

    • CommentRowNumber2.
    • CommentAuthorGuest
    • CommentTimeJan 20th 2021
    Proposition 3.1. A limit in an under category is computed as a limit in the underlying category.

    This formulation is really misleading. It is not difficult to construct examples of categories without limits in which every coslice does have a limit, e.g. finite sets with surjections.
    It would be proper, in my opinion, to remove it, leaving only the "precisely"-part, or reformulate:

    Proposition 3.1. If limits exist in the underlying category then the same is true for every under category and these limits coincide.

    Rostislav Matveev
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJan 20th 2021

    Sure, I have adjusted the wording.

    But the exposition of this whole proposition leave much room for improvement. You should feel invited to edit it or re-write it from scratch.

    diff, v18, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 5th 2023

    I have expanded the example on pointed objects (here)

    diff, v19, current

  1. Added the example of the category of pointed modules being the coslice category under the additive group of the ground ring

    Joachim Joszef

    diff, v20, current

  2. Use a more standard notation for the coslice category.

    Mark John Hopkins

    diff, v22, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeAug 7th 2023

    added reference to:

    With that, the ratio of references in the entry that agree with your notation over those who agree with the notion you deleted is zero.

    (In other words: At least make some constructive edit, like adding a reference.)

    diff, v24, current