Timeline for Computing homotopy (co)limits in a nice simplicial model category?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Feb 11, 2012 at 23:03 | vote | accept | dhagbert | ||
| Feb 8, 2012 at 14:44 | history | edited | Charles Rezk | CC BY-SA 3.0 |
typo
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| Feb 8, 2012 at 14:43 | comment | added | Charles Rezk | @Dylan. Most probably, yes. | |
| Feb 8, 2012 at 4:49 | comment | added | Dylan Wilson | @Charles: Did you mean J(-, j) instead of J(j, -)? I thought the first variable had to be a contravariant functor... | |
| Feb 7, 2012 at 10:47 | comment | added | Justin Noel | I would like to add Dugger's primer on homotopy colimits pages.uoregon.edu/ddugger/hocolim.pdf to this extended bibliography. Although incomplete it does compare many notions of homotopy colimit in a single place. | |
| Feb 6, 2012 at 22:26 | comment | added | Mike Shulman | Some more recent references are Hirschorn's book "Model categories and their localizations", my own paper "Homotopy limits and colimits and enriched homotopy theory" (arxiv), and "Weighted limits in simplicial homotopy theory" (web) by Nicola Gambino. | |
| Feb 6, 2012 at 19:04 | history | edited | Charles Rezk | CC BY-SA 3.0 |
remark about simplicial objects
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| Feb 6, 2012 at 18:24 | comment | added | dhagbert | Thank you. In the special case that interests me, $J$ I suppose is $\Delta^{op}$ and $P$ is simplicial presheaves with the model structure in which weak equivalences and cofibrations are defined level-wise. Then I think everything is cofibrant in $P$ (?), so that seems not a problem. I'm not sure what $J(j,k)$ looks like, though. I suppose you include $\Delta^{op}$ into simplicial sets and take mapping spaces there? Other easy examples: what if $J$ is the corner of a push-out or of a pull-back. How to enrich $J$? | |
| Feb 6, 2012 at 16:41 | history | answered | Charles Rezk | CC BY-SA 3.0 |