Timeline for Left Kan extension along Yoneda of pullback-preserving functor preserving pullbacks
Current License: CC BY-SA 4.0
11 events
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| Dec 3, 2019 at 20:30 | history | edited | Simon Henry | CC BY-SA 4.0 |
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| Feb 24, 2019 at 18:41 | comment | added | Tim Campion | Oh I see. I misunderstood your point about $D$ not needing finite limits. Sorry! | |
| Feb 24, 2019 at 18:40 | comment | added | Simon Henry | @TimCampion Of course, but I don't think I said that. $C$ was assumed to have pullback in the question, and I added the assumption that it has a terminal object, so all finite limits. | |
| Feb 24, 2019 at 17:53 | comment | added | Tim Campion | Nice! One quibble: it is not the case that if $F: C \to Set$ preserves finite limits then $F_!: Psh(C) \to Set$ preserves finite limits -- the hypothesis that $C$ has finite limits is really necessary. For instance let $C$ be the discrete category with two objects, and let $F$ send both to a one-element set. Then $Psh(C) = Set^2$, and $F_! (A,B) = A \amalg B$. The functor $F$ preserves finite limits, but $F_!$ fails to preserve the terminal object for instance. | |
| May 20, 2018 at 15:00 | vote | accept | Alexander Körschgen | ||
| May 1, 2018 at 7:48 | history | edited | Simon Henry | CC BY-SA 3.0 |
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| May 1, 2018 at 7:31 | history | edited | Simon Henry | CC BY-SA 3.0 |
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| May 1, 2018 at 7:25 | history | edited | Simon Henry | CC BY-SA 3.0 |
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| Apr 30, 2018 at 18:57 | history | edited | Simon Henry | CC BY-SA 3.0 |
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| Apr 30, 2018 at 18:41 | history | edited | Simon Henry | CC BY-SA 3.0 |
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| Apr 30, 2018 at 16:33 | history | answered | Simon Henry | CC BY-SA 3.0 |