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Started weak equivalence of internal categories. Needs some more work, including examples and theorems.
In a topos one takes epis, not regular epis for $J$ ?
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).
In a topos every epimorphism is regular (and effective)!
[edit: I see I overlapped with David.]
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”.
Thanks, Urs.
Oh, and I have added the Context-table of contents internal categories.
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