Timeline for How should I think about concrete functors and in particular about concrete isomorphism?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Dec 27, 2019 at 15:41 | comment | added | Todd Trimble | My answer has just been downvoted. I invite the downvoter to explain why. | |
| Aug 1, 2019 at 11:59 | comment | added | Todd Trimble | I don't know of any general such criterion. A trouble is that considering the fibers abstractly on their own loses the information of how they are "woven together" via the underlying-set functor. But an enhanced criterion in this vein holds for fibrations, where you could say that two fibrations over $C$ are concretely equivalent if their associated fiber functors $C \to Cat$ are naturally equivalent. | |
| Aug 1, 2019 at 7:14 | comment | added | user57432 | Does there exist any criteria of two categories being concretely isomorphic in terms of fibre subcategories? It seems that (and I now came to realize this after going through the example given in The Joy of Cats) that if two concrete categories are concretely isomorphic then their fibre subcategories must also be isomorphic (i.e., roughly the "number" of structured objects over the base category should be same and the "number" of relations they are in should also be same). Is this a good intuition? | |
| Aug 1, 2019 at 3:40 | vote | accept | CommunityBot | ||
| Jul 31, 2019 at 19:11 | history | answered | Todd Trimble | CC BY-SA 4.0 |