Timeline for Monoidal tensor product which preserves directed limits
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Sep 5, 2017 at 0:38 | vote | accept | Bert Lindenhovius | ||
| Sep 4, 2017 at 19:29 | history | edited | Bert Lindenhovius | CC BY-SA 3.0 |
Fixed the terminology "directed limit" which seems to be incorrect. Furthermore, addition of some emphasis on the properties that M should have.
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| Sep 1, 2017 at 0:59 | answer | added | Tim Campion | timeline score: 5 | |
| Jul 14, 2017 at 6:09 | comment | added | Kevin Carlson | At least for the simplest Day convolution, that is, the cartesian product of sets, it seems to me that cofiltered limits (in particular, directed limits) are preserved by products. (The limit of the diagram $(D_i\times S)$ as $i$ varies over some index category is a set of families $((d_i,s_i))$, but the $s_i$ must all be equal, by cofilteredness.) I guess all this really requires is that the diagram shape be connected. | |
| Jul 11, 2017 at 19:13 | comment | added | Todd Trimble | Oh, sorry for misreading! | |
| Jul 11, 2017 at 19:10 | history | edited | Bert Lindenhovius | CC BY-SA 3.0 |
added 25 characters in body
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| Jul 11, 2017 at 19:07 | comment | added | Bert Lindenhovius | Thank you. However, we need preservation of limits, not of colimits. I'll edit my post to avoid confusion. | |
| Jul 11, 2017 at 19:02 | comment | added | Todd Trimble | It is well-known that for the Day convolution, $A \otimes -$ preserves all colimits, not just directed colimits. | |
| Jul 11, 2017 at 18:59 | history | asked | Bert Lindenhovius | CC BY-SA 3.0 |