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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• 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 $J$ ?

• 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 $J$ has to be subcanonical (for example, take the pretopology on $Top$ 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