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Timeline for Existence of "good" concretizations

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Jul 31, 2019 at 16:17 comment added Ivan Di Liberti Also, if this "forgetful" functor preserves wide pullbacks and the category is sufficiently complete, then it has a generating set.
Apr 11, 2012 at 17:46 comment added Qiaochu Yuan For what it's worth, it's straightforward to exhibit a monomorphism-preserving-concretizable category with no generating set; just take any groupoid which is not equivalent to a small groupoid, e.g. the category of sets and isomorphisms.
Apr 10, 2012 at 18:16 history answered Andreas Blass CC BY-SA 3.0