Timeline for How to construct a free 2-group on a groupoid?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Feb 25, 2016 at 17:03 | history | edited | Ronnie Brown | CC BY-SA 3.0 |
explanation of an error
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| Feb 16, 2016 at 12:25 | comment | added | Fernando Muro | As you know, this passage from crossed modules to groupoids is equivalent to taking the loop space. The 'free object' Tom asks about is the 2-type of the suspension. | |
| Feb 16, 2016 at 10:38 | comment | added | Ronnie Brown | @Fernando: Interesting. What is the topological significance of what you suggest? | |
| Feb 15, 2016 at 0:36 | comment | added | Fernando Muro | I mean crossed module of groups. | |
| Feb 14, 2016 at 23:30 | comment | added | Fernando Muro | I think that the notion of freeness Tom is talking about is not related to induced crossed modules. The functor he has in mind is not your $\Phi$. In the language of crossed modules, his forgetful functor is the one sending a crossed module $\partial\colon M\rightarrow N$ to the category $M\rtimes N\rightrightarrows N$. | |
| Feb 14, 2016 at 17:45 | history | edited | Ronnie Brown | CC BY-SA 3.0 |
changed one cofibration to cocartesian
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| Feb 14, 2016 at 12:25 | history | edited | Ronnie Brown | CC BY-SA 3.0 |
added an extra explanation in answer to Fernando's comment
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| Feb 14, 2016 at 11:43 | comment | added | Ronnie Brown | See also the notion of free crossed module (over groupoids) on a morphism of groupoids and also Appendix B3 of the NAT book on cofibrations of categories. I'm working up an answer in these terms. | |
| Feb 14, 2016 at 11:14 | comment | added | Ronnie Brown | @Fernando : How is this notion of freeness related to the concept of induced crossed module, discussed in various parts of the EMS book? The "globular" paper HHA, 10 (2008), No. 1, pp.327-343.does not discuss induced constructions, but it does give a globular colimit theorem. | |
| Feb 10, 2016 at 7:08 | comment | added | Fernando Muro | Ronnie I think that this notion of freeness is unrelated to the notion Tom is asking about. | |
| Feb 9, 2016 at 21:17 | history | edited | Ronnie Brown | CC BY-SA 3.0 |
bit more explanation at end
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| Feb 7, 2016 at 10:53 | history | edited | Ronnie Brown | CC BY-SA 3.0 |
typo
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| Feb 6, 2016 at 22:23 | history | answered | Ronnie Brown | CC BY-SA 3.0 |