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    • CommentRowNumber1.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 17th 2012

    Started weak equivalence of internal categories. Needs some more work, including examples and theorems.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeMay 17th 2012

    In a topos one takes epis, not regular epis for JJ ?

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 17th 2012

    All epis are regular in a topos. In a regular category you take regular epis. Although there is nothing that says JJ has to be subcanonical (for example, take the pretopology on TopTop of locally split maps).

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 17th 2012
    • (edited May 17th 2012)

    In a topos every epimorphism is regular (and effective)!

    [edit: I see I overlapped with David.]

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMay 17th 2012

    I have added pointers to the entry from internal category and equivalence of categories. I have also added under Related concepts a pointer to anafunctor, which I guess you may want to come back to. Notice that at internal category there is a paragraph on “ana-equivalences”.

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 17th 2012

    Thanks, Urs.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeMay 17th 2012

    Oh, and I have added the Context-table of contents internal categories.

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