Timeline for Homotopy of functors
Current License: CC BY-SA 4.0
11 events
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| Jan 2, 2020 at 0:13 | vote | accept | CommunityBot | ||
| Jan 1, 2020 at 21:28 | answer | added | Peter May | timeline score: 7 | |
| Jan 1, 2020 at 17:27 | history | edited | user147820 | CC BY-SA 4.0 |
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| Dec 31, 2019 at 1:54 | history | edited | user147820 | CC BY-SA 4.0 |
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| Dec 30, 2019 at 17:01 | comment | added | Ronnie Brown | @Harry Grindi I should say that T&G still seems to be the only algebraic topology book in English to use the idea of a set of base points for use in descent situations re Van Kampen's theorem, as strongly supported by Grothendieck in his Esquisse. Whether the simplicial approach is the "best" is another matter. Some motivitic homotopy work uses cubical sets with connections, for technical reasons that the simplicial did not work. See my 2018 paper in Indag. | |
| Dec 30, 2019 at 15:23 | comment | added | Ronnie Brown | It is a case of horses for courses. In the case of functors to groupoids or strict higher groupoids, then the approach of my book, and its sequel, Nonabelian Algebraic Topoology, , is often convenient. | |
| Dec 30, 2019 at 4:40 | comment | added | Harry Gindi | I think that both of these references are more or less obsolete. The first notion you're referring to is fleshed out in detail in the Asterisque 301 volume by Georges Maltsiniotis. Note that this all lives in a world where categories model spaces. The other construction does not make sense in general and uses the homotopy structure on Top in an essential way. In that case, take a look at the appendices of Higher Topos Theory or Hirschhorn's book in the section on simplicial model categories. | |
| Dec 30, 2019 at 4:17 | history | edited | user147820 | CC BY-SA 4.0 |
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| Dec 30, 2019 at 3:51 | history | edited | user147820 | CC BY-SA 4.0 |
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| Dec 30, 2019 at 3:43 | history | edited | user147820 | CC BY-SA 4.0 |
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| Dec 30, 2019 at 3:21 | history | asked | user147820 | CC BY-SA 4.0 |