Timeline for Kan extensions of pseudofunctors
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Oct 31, 2017 at 4:02 | answer | added | Mike Shulman | timeline score: 1 | |
| Jun 15, 2016 at 2:08 | comment | added | Fernando | Sorry for the delayed comment. I just saw your question now (I am sorry about that). But I had worked out the concept of pointwise pseudo-Kan extensions: actually, I gave a talk mentioning them at University of Aveiro (CT 2015). I have two papers mentioning pseudo-Kan extensions. One was published "On Biadjoint Triangles" (TAC) and the other one can be found in CMUC's preprints (16-30). On one hand, conical bilimits do not work in general. On the other hand, the "formula" for pointwise right pseudo-Kan extensions is pretty similar to the pointwise right Kan extensions (via weighted bilimits | |
| Sep 1, 2015 at 21:53 | history | edited | James Waldron | CC BY-SA 3.0 |
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| Sep 1, 2015 at 21:52 | comment | added | Zhen Lin | It depends on what you mean. As Finn Lawler explained, you only need (pseudo)colimits of diagrams of shape $\mathcal{A}$ weighted by certain (pseudo)functors. Whether you can reduce to conical (pseudo)colimits or not depends on the weights – specifically, whether the weights themselves can be reduced to conical (pseudo)colimits of representables. | |
| Sep 1, 2015 at 21:44 | comment | added | James Waldron | @ZhenLin: I see, thank you. In the case I am particularly interested in, $\mathscr A$ is in fact a 1-category, so perhaps the potential formula only involves pseudo colimits indexed by a 1-category? (I have edited the question). | |
| Sep 1, 2015 at 21:37 | comment | added | James Waldron | @DavidWhite: Also, the categories there are 'enriched' rather that 'weakly enriched', as in the case of bicategories. | |
| Sep 1, 2015 at 21:31 | comment | added | James Waldron | @DavidWhite: Yes, I have looked in Riehl's book. Kan extensions of enriched functors between enriched categories are covered there, but as far as I can tell everything is done for strict and not pseudo functors. | |
| Sep 1, 2015 at 17:59 | answer | added | Finn Lawler | timeline score: 4 | |
| Sep 1, 2015 at 16:11 | comment | added | Zhen Lin | The "standard" formula doesn't generalise well. You would be better off starting with the formula from enriched category theory in terms of weighted colimits. | |
| Sep 1, 2015 at 12:22 | comment | added | David White | Have you looked at Emily Riehl's book yet? My gut instinct is that she would take this approach. | |
| Sep 1, 2015 at 11:08 | review | First posts | |||
| Sep 1, 2015 at 11:26 | |||||
| Sep 1, 2015 at 11:06 | history | asked | James Waldron | CC BY-SA 3.0 |