Timeline for Original reference for categories of presheaves as free cocompletions of small categories
Current License: CC BY-SA 4.0
16 events
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| Jun 13 at 11:28 | history | edited | varkor | CC BY-SA 4.0 |
Added an earlier reference.
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| Dec 24, 2021 at 21:39 | history | edited | varkor | CC BY-SA 4.0 |
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| Dec 24, 2021 at 21:37 | comment | added | varkor | @SimonPepinLehalleur: thank you for this reference. I agree that it seems likely they knew about the presheaf case in light of this proposition, and it's certainly an earlier reference for some form of cocompletion based on presheaves. | |
| Dec 24, 2021 at 21:09 | comment | added | Simon Pepin Lehalleur | This statement looks like it should be in SGA4, but as far as I can tell it isn't. It comes close though, in Exposé I Proposition 8.7.3 they prove the analoguous statement for Ind-objects and filtered colimit preserving functors, and it seems likely that they knew about the presheaf case. | |
| Oct 12, 2021 at 12:31 | history | edited | varkor | CC BY-SA 4.0 |
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| Oct 12, 2021 at 12:29 | comment | added | varkor | @RoaldKoudenburg: thank you! Day and Lack cite a different paper of Lidner's, "Enriched categories and enriched modules", which had confused me as the result does not seem to appear there. It seems they cited the wrong paper. Thanks for digging this up! | |
| Oct 12, 2021 at 12:12 | comment | added | Roald Koudenburg | In "Limits of small functors" (2007) Day and Lack credit "V-enriched small presheaves giving the free small-cocompletion of large V-categories" as due to Lindner. As I understand it they refer to theorem 2.11 of Lindner's "Morita equivalences of enriched categories" (1974). Lindner cites Ulmer's paper for the unenriched version of this result. | |
| Jul 7, 2021 at 1:28 | history | edited | varkor | CC BY-SA 4.0 |
Added reference to Kelly's *Basic concepts*.
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| Jul 6, 2021 at 22:08 | comment | added | varkor | @AlexanderCampbell: thanks for that, I can't believe I didn't check Basic concepts. It seems it was part of the categorical folklore in some places, but perhaps not others, then. | |
| Jul 6, 2021 at 22:04 | comment | added | Alexander Campbell | The result is much older than Pitts’ 1985 paper and was absolutely part of the categorical folklore before then. For example, it is Theorem 4.51 in Kelly’s 1982 book tac.mta.ca/tac/reprints/articles/10/tr10abs.html, and it is surely in Gabriel-Ulmer’s 1971 SLN volume, and also probably in SGA4. (I don’t have the last two references handy so can’t confirm at the moment.) | |
| Jul 6, 2021 at 15:42 | comment | added | varkor | @MartinBrandenburg: apologies to making the context of the comments confusing by updating the answer! And I agree with your comment about novelty. | |
| Jul 6, 2021 at 15:30 | comment | added | Martin Brandenburg | My comment refered to the 1st version of the answer and thus to Pitts' paper. Regarding your edit: Okay, so it's not my personal fault that I never know if one of my results is new or not. It happened all the time, even to the pioneers in the field. | |
| Jul 6, 2021 at 13:17 | history | edited | varkor | CC BY-SA 4.0 |
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| Jul 5, 2021 at 21:11 | comment | added | Martin Brandenburg | This is cool! I always wondered where the statement of Lemma 1.1 appeared in the literature (I have used this from time to time). But Pitts doesn't prove that the two 2-functors are inverse to each other. What a pitty. | |
| Jul 5, 2021 at 14:59 | vote | accept | varkor | ||
| Jul 5, 2021 at 14:36 | history | answered | varkor | CC BY-SA 4.0 |