Timeline for Is this a characterization of cocompleteness?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 31, 2018 at 15:41 | comment | added | Tim Campion | Actually, it's natural to guess that the answer is no if you don't assume pointwiseness. This might be a candidate example statement for the point of pointwise Kan extensions... | |
| Mar 31, 2018 at 15:40 | vote | accept | Ivan Di Liberti | ||
| Mar 31, 2018 at 15:40 | comment | added | Ivan Di Liberti | This is because I didn't know how to say that there are pointwise without colimits. Thanks for your answer. | |
| Mar 31, 2018 at 15:39 | comment | added | Tim Campion | There are many ways to say that an extension is poinwise. One way is to say that the Kan extension is preserved by representable functors. But now I see I did not read carefully enough -- although you mention that the extension is pointwise in the cocomplete case, you didn't assume it in your question statement. | |
| Mar 31, 2018 at 15:36 | history | edited | Tim Campion | CC BY-SA 3.0 |
added 126 characters in body
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| Mar 31, 2018 at 15:36 | comment | added | Ivan Di Liberti | Since I am not assuming that A has colimits, how can I say that the extension is pointwise? | |
| Mar 31, 2018 at 15:34 | history | answered | Tim Campion | CC BY-SA 3.0 |