Timeline for What's the intuition for weighted limits?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Dec 2, 2022 at 19:07 | comment | added | MrPajeet | @MartinBrandenburg could you give some intuition as to how tensor products and weighted limits are related? I have read some functor tensor product in terms of a coend formula, say from Riehl's book Categorical Homotopy theory. Coends I interpret as the object closest from the 'double system', i.e., as an average of some sort. | |
| Nov 16, 2022 at 20:02 | vote | accept | MrPajeet | ||
| Nov 14, 2022 at 2:31 | comment | added | Martin Brandenburg | @SergeiAkbarov At the moment I am not able to write a good expository account on this. Others will do better. | |
| Nov 12, 2022 at 9:15 | history | became hot network question | |||
| Nov 12, 2022 at 6:56 | comment | added | display llvll | @SergeiAkbarov the universal property of a weighted colimit is really the universal property of a tensor product. In particular, if you see two modules M,N as Ab-functors on a ring (seeing the ring a as an Ab-category with one object) then the Ab-weighted colimit of M weighted by N is their tensor product as modules. | |
| Nov 12, 2022 at 6:08 | comment | added | Sergei Akbarov | @MartinBrandenburg I think you should post an answer here with the detailed explanation of this. | |
| Nov 12, 2022 at 3:20 | comment | added | Martin Brandenburg | I see weighted colimits as natural generalizations of tensor products. Hence, weighted limits as cotensor products. See my preprint on bicategorical colimits for more on this (arXiv:2001.10123). Actually when you change the notation a bit, the analogy becomes very clear. | |
| Nov 12, 2022 at 1:57 | answer | added | Zhen Lin | timeline score: 12 | |
| Nov 12, 2022 at 1:35 | history | edited | MrPajeet | CC BY-SA 4.0 |
added 338 characters in body
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| Nov 12, 2022 at 1:15 | history | asked | MrPajeet | CC BY-SA 4.0 |