Timeline for Which free strict $\omega$-categories are also free as weak $(\infty,\infty)$-categories?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 22, 2021 at 19:23 | answer | added | Tim Campion | timeline score: 2 | |
| Mar 2, 2020 at 4:24 | answer | added | Simon Henry | timeline score: 5 | |
| Mar 2, 2020 at 4:22 | comment | added | Harry Gindi | One final comment, I think you could prove (with a lot of combinatorial work) the statement for 2-polygraphs using some of the recent work by Alex Campbell on (∞,2)-categories. I think (∞,n) is probably out of reach, however. | |
| Mar 2, 2020 at 4:05 | comment | added | Harry Gindi | The reason why this is highly problematic even for Steiner's diagrams is that cells are glued into cells freely generated in a lower dimension, then you have to generate more cells, then glue again, etc., and things get really crazy when you have to glue in cells along whiskerings. | |
| Mar 2, 2020 at 3:55 | comment | added | Harry Gindi | I'm also interested in an answer to this question, but I think it's wide open. I tried working it out at one point, but I didn't get anything super nice. Free strict ω-categories on globular sets do work, but this is not enough to get loop-free Steiner complexes. I suspect that the answer might be free strict ω-categories on a polygraph (which does include Steiner complexes), but things get really hairy really fast. You would have to show levelwise that each free n-category on the n-1-polygraph can be constructed by gluing in higher dimensional analogues of horns. | |
| Mar 2, 2020 at 2:09 | history | edited | Tim Campion | CC BY-SA 4.0 |
edited title
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| Mar 2, 2020 at 2:01 | history | edited | Tim Campion | CC BY-SA 4.0 |
added 192 characters in body
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| Mar 2, 2020 at 1:56 | history | asked | Tim Campion | CC BY-SA 4.0 |