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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 23rd 2012

    added at core the remark that the core is right adjoint to the forgetful functor GrpdCatGrpd \to Cat.

    • CommentRowNumber2.
    • CommentAuthorYuxi Liu
    • CommentTimeJul 1st 2020

    added some examples

    diff, v9, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJul 2nd 2020

    Thanks for contributing.

    Let’s make such lists of examples into bullet-item lists, for ease of discerning them, like so:

      * Given a [[preorder|preordered set]], regarded as a category, taking its core is the same as partitioning the set into equivalence classes of the preorder.
    
      * A combinatorial [[species]] is defined as a [[presheaf]], that is, a contravariant functor to Set, on the core of [[FinSet]].
    

    Your last line added here was:

    Every groupoid has a contravariant functor to itself. It preserves the objects and sends the arrows to their inverses.

    But I don’t see how that is an example for the page “core”?

    diff, v10, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeDec 29th 2021

    gave the entry and Idea-section, highlighting the adjointness and making clear that the concept exist in the full generality of (n,r)(n,r)-categories. Added pointer to

    (all this was previously hinted at only rather indirectly through a pointer to category object in an (infinity,1)-category towards the end).

    diff, v12, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeDec 29th 2021

    gave the entry and Idea-section, highlighting the adjointness and making clear that the concept exist in the full generality of (n,r)(n,r)-categories. Added pointer to

    (all this was previously hinted at only rather indirectly through a pointer to category object in an (infinity,1)-category towards the end).

    diff, v12, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeDec 29th 2021

    Sorry for the duplicate. Am having much trouble with timeouts when saving, as of late.

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