Timeline for Abstract Relation between Presehaves and Simplicial Sets
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Nov 4, 2011 at 17:58 | comment | added | Spice the Bird | @peter: I think I see what the OP means by saying that a kan complex is like a glueing condition. Suppose that you have two n-simplices glued about a face. Then we may map the two simplices glued about a face into some horn (a horn with some faces removed). The composite of the two simplicies glued into the horn, then into the n+1 simplex is a cofibration. Thus we may lift it to a map from he n-simplex. Just a Guess. | |
| Nov 17, 2009 at 22:34 | vote | accept | Konrad Voelkel | ||
| Nov 13, 2009 at 1:10 | comment | added | Peter Arndt | No, I mean actually equivalent. "Quillen equivalent" is a notion for model categories, i.e. categories having all this extra structure but in which you have not yet inverted the "weak equivalences". If you then invert these you get the "homotopy category" of the model category. Quillen equivalence of two model categories implies equivalenc of their homotopy categories - in general it is not itself an equivalence of categories! The statements in the last two paragraphs relate the homotopy categories to other, equivalent, categories - no model structures are involved there. | |
| Nov 12, 2009 at 23:17 | comment | added | Konrad Voelkel | Do you mean "Quillen equivalent" when you say "equivalent"? | |
| Nov 12, 2009 at 21:49 | history | answered | Peter Arndt | CC BY-SA 2.5 |