Timeline for Internal Day convolution
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 16, 2016 at 16:12 | answer | added | Mike Shulman | timeline score: 2 | |
| Oct 21, 2013 at 11:16 | vote | accept | Michal R. Przybylek | ||
| May 7, 2013 at 19:40 | answer | added | Michal R. Przybylek | timeline score: 5 | |
| Apr 22, 2013 at 19:58 | history | edited | Michal R. Przybylek | CC BY-SA 3.0 |
added finite cocompleteness after the comment of Alex Simpson
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| Apr 22, 2013 at 14:43 | comment | added | Michal R. Przybylek | @Zhen, thank you --- $\textbf{FinSet}$ is a very good example to see why the external cocompleteness is not necessary here (since $\textbf{FinSet}$-internal categories are finite, the coend in the Day convolution may be expressed via finite colimits). | |
| Apr 22, 2013 at 14:31 | comment | added | Michal R. Przybylek | @Alex, you are right that for some of these constructions we have to assume that $\mathbb{C}$ has finite colimits (coequalisers suffice) --- thank you, I will update the question. | |
| Apr 22, 2013 at 14:27 | comment | added | Zhen Lin | A locally cartesian closed category with finite colimits believes itself to be cocomplete (in the internal sense, of course). Caution: such categories may suffer from delusions; $\textbf{FinSet}$ is one example. | |
| Apr 22, 2013 at 12:09 | comment | added | Alex Simpson | The co-end formula in the Day convolution is a form of colimit, and I can see no reason for the relevant colimit to be available when the containing category is a general local cartesian-closed category. Shouldn't some cocompleteness assumption be added? | |
| Apr 22, 2013 at 7:33 | history | edited | Michal R. Przybylek | CC BY-SA 3.0 |
fixed grammar and corrected typo in the formula of convolution
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| Apr 21, 2013 at 20:00 | history | edited | Michal R. Przybylek | CC BY-SA 3.0 |
reference to cosmoi of internal categories added
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| Apr 21, 2013 at 18:10 | history | asked | Michal R. Przybylek | CC BY-SA 3.0 |