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Jul 9, 2021 at 19:22 comment added Peter LeFanu Lumsdaine @IvanDiLiberti: There are plenty of “decent” categories without equalisers, though — including in particular most categories of manifolds.
Jul 9, 2021 at 13:42 comment added Ivan Di Liberti True, but in a decent category this also implies faithfulness. A conservative functor preserving equalizers in a category with equalizers is also faithful.
Jul 9, 2021 at 13:39 history edited Tim Campion CC BY-SA 4.0
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Jul 8, 2021 at 23:52 comment added Martin Brandenburg We just need that $\hom(-,I)$ is conservative.
Jul 8, 2021 at 14:41 comment added Ivan Di Liberti This is cute. Upvote.
Jul 8, 2021 at 11:50 history answered Tim Campion CC BY-SA 4.0