Timeline for Spectra and localizations of the category of topological spaces
Current License: CC BY-SA 2.5
10 events
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| Feb 24, 2010 at 6:16 | history | edited | Reid Barton | CC BY-SA 2.5 |
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| Feb 24, 2010 at 6:06 | comment | added | Reid Barton | I don't know of a specific place where it is written down, but invertibility of an endofunctor is an (∞,1)-categorical (as opposed to (∞,2)-categorical) notion, so it's directly analogous to the situation in classical algebra. | |
| Feb 24, 2010 at 6:03 | history | edited | Reid Barton | CC BY-SA 2.5 |
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| Feb 24, 2010 at 5:42 | comment | added | Dmitri Pavlov | Is the operation of adjoining an inverse to an endofunctor explained somewhere in Lurie's papers or anywhere else? | |
| Feb 24, 2010 at 5:38 | vote | accept | Dmitri Pavlov | ||
| Feb 24, 2010 at 5:28 | comment | added | Reid Barton | I should have mentioned that I'm working in the world of presentable (∞,1)-categories. I'm pretty sure my new statement is correct. | |
| Feb 24, 2010 at 5:23 | comment | added | Tyler Lawson | It's even worse than that, you only get the category of suspension spectra. Also, I had some other argument written here about inverting the loop functor which suffered from me accidentally getting an adjunction on the wrong side. Remember, kids: no Math Overflow late at night. | |
| Feb 24, 2010 at 5:01 | history | edited | Reid Barton | CC BY-SA 2.5 |
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| Feb 24, 2010 at 4:39 | comment | added | Chris Schommer-Pries | Minor quible. Don't you only get connective spectra by starting with Top and inverting the suspension functor? Also a question: If you start with Top and invert the loops functor do you also get the category of (connective) spectra? | |
| Feb 24, 2010 at 4:25 | history | answered | Reid Barton | CC BY-SA 2.5 |