Timeline for (Co)limits of locally cartesian closed categories
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 10, 2017 at 22:17 | vote | accept | John Berman | ||
| Dec 10, 2017 at 17:58 | comment | added | Tim Campion | @FoscoLoregian What 2-category do you consider precisely? I think some care is warranted because if I recall correctly, the obvious 2-category of cartesian closed categories is not 2-monadic over the 2-category $Cat$, but the obvious groupoid-enriched category of cartesian closed categories is monadic in the groupoid-enriched sense over $Cat$ considered as a groupoid-enriched category. | |
| Dec 10, 2017 at 17:43 | answer | added | Tim Campion | timeline score: 5 | |
| Dec 10, 2017 at 16:30 | answer | added | Anton Fetisov | timeline score: 3 | |
| Dec 10, 2017 at 15:17 | history | edited | John Berman | CC BY-SA 3.0 |
added 22 characters in body
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| Dec 10, 2017 at 7:15 | answer | added | Karol Szumiło | timeline score: 5 | |
| Dec 9, 2017 at 22:55 | comment | added | fosco | @AntonFetisov "Dist is too large to be presentable" tell us more. There's always an opportunity to learn something new about size issues. | |
| Dec 9, 2017 at 22:52 | comment | added | fosco | I mean presentable as a $\bf Cat$-enriched category as in Kelly, Borceux, Rosicky and others; the definition resembles the classical one but is different (and behaves differently) in subtle ways. I wouldn't bet the farm on the fact that $\bf sSet$-enriched presentable categories correspond to presentable $\infty$-categories via Quillen equivalence. (Let me put it differently: I would like to see the proof) | |
| Dec 9, 2017 at 22:39 | comment | added | John Berman | @FoscoLoregian If I am right about what Cat-presentable means, I think that is more or less what I want to prove. | |
| Dec 9, 2017 at 22:36 | comment | added | John Berman | @AntonFetisov That sounds intriguing, but this 2-category of distributors is new to me, so I don't know what you mean by a "tensor representation of some tensor category." | |
| Dec 9, 2017 at 22:23 | comment | added | fosco | Is it possible to (dis)prove that the 2-category $\bf LCC$ is a $\bf Cat$-presentable category? | |
| Dec 9, 2017 at 20:07 | comment | added | Anton Fetisov | I'd have a very simple proof of this statement if the 2-category of distributors would be locally presentable: encode lcc structure as a tensor representation of some tensor category in $Dist$, then some general facts about operads should be sufficient. Unfortunately $Dist$ is too large to be presentable. Maybe there is a way to state some size filtration on it which would filter $LCC$ by presentable subcategories? | |
| Dec 9, 2017 at 19:59 | comment | added | John Berman | Yes, that's what I mean. | |
| Dec 9, 2017 at 18:48 | comment | added | Anton Fetisov | Does "presentable" mean the same as "locally presentable"? | |
| Dec 9, 2017 at 14:38 | history | asked | John Berman | CC BY-SA 3.0 |