Timeline for The symmetric monoidal closed structure on the category of $\mathcal{F}$-cocomplete categories and $\mathcal{F}$-cocontinuous functors
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Jan 23, 2020 at 11:35 | vote | accept | Ivan Di Liberti | ||
| Jan 23, 2020 at 11:33 | answer | added | Martin Brandenburg | timeline score: 3 | |
| Jan 23, 2020 at 10:43 | comment | added | Martin Brandenburg | One doesn't need monads to understand Kelly's tensor product. Q3 is probably answered in core.ac.uk/download/pdf/82548027.pdf | |
| Jan 21, 2020 at 22:09 | comment | added | Ivan Di Liberti | Looking a bit closer to the paper, the fact that everything is strict might be a problem in this case. Maybe this is fixable, I will think about it. | |
| Jan 21, 2020 at 21:57 | comment | added | Ivan Di Liberti | Thank you very much! I remember John mentioned me the paper of Hyland and Power, but he did not mention to me his own paper! I think this might really be an answer to my question! | |
| Jan 21, 2020 at 21:04 | comment | added | Noam Zeilberger | @IvanDiLiberti have you seen Bourke's paper on Skew structures in 2-category theory and homotopy theory? Section 6 discusses a 2-dimensional version of Kock's result due to Hyland and Power, which Bourke argues is nicely analyzed via a skew closed structure on the 2-category $T\text{-}\mathrm{Alg}_s$ of algebras and strict morphisms. | |
| Jan 21, 2020 at 17:59 | answer | added | Giorgio Mossa | timeline score: 4 | |
| Jan 21, 2020 at 17:51 | history | edited | Ivan Di Liberti | CC BY-SA 4.0 |
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| Jan 21, 2020 at 17:31 | comment | added | Ivan Di Liberti | @SimonHenry, I hope I finally managed to give a good reference. Seal does not show that it is monoidal closed, because he does not assume closedness of the base, yet he proves monoidality of the Eilenberg-More category of algebras. No assumption on presentability is needed. I believe that if the base is closed, so is the EM-category. | |
| Jan 21, 2020 at 17:29 | history | edited | Ivan Di Liberti | CC BY-SA 4.0 |
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| Jan 21, 2020 at 17:04 | history | edited | Ivan Di Liberti | CC BY-SA 4.0 |
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| Jan 21, 2020 at 17:02 | comment | added | Simon Henry | I think the reference you gave only show that the category of algebra is a "closed category", it does not show it is monoidal. I will be tempted to think that to get a monoidal category of algebras you need some presentabitliy/accessibility assumption, or at least cocompletness. In the case of interest to you this result only gave you that functor categories are $\mathcal{F}$-cocomplete, which you already know. | |
| Jan 21, 2020 at 16:49 | comment | added | Ivan Di Liberti | @SimonHenry, thanks. I edited. | |
| Jan 21, 2020 at 16:49 | history | edited | Ivan Di Liberti | CC BY-SA 4.0 |
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| Jan 21, 2020 at 16:28 | comment | added | Simon Henry | Could you give a reference for Kock's results ? he has several paper on strong & commutative monads and I can't find the one where this theorem is... | |
| Jan 21, 2020 at 15:41 | history | edited | Ivan Di Liberti | CC BY-SA 4.0 |
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| Jan 21, 2020 at 14:46 | history | edited | Ivan Di Liberti | CC BY-SA 4.0 |
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| Jan 21, 2020 at 14:27 | history | asked | Ivan Di Liberti | CC BY-SA 4.0 |