Timeline for Site dependance of the Cech weak equivalences on simplicial sheaves
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 27, 2014 at 18:36 | comment | added | David Carchedi | I learned this from Jacob Lurie: Let $Q=\prod_i I$ be the hilbert cube. Consider all the open subsets which are homeomorphic to $Q \times [0,1)$. These form a basis, but are not closed under finite intersections. Considering them as a subcategory of the poset of all open subsets, one can define an obvious site structure. However, infinity sheaves on this site is different than infinity sheaves on the Hilbert cube. | |
| Nov 27, 2014 at 18:19 | comment | added | Simon Henry | More precisely, my question was: "do you know if there is a known example of two sites of definition of T which yields different infini topos ?" | |
| Nov 27, 2014 at 18:16 | comment | added | David Carchedi | There has to be, since assuming there is no counterexample, one could show that both sites yield the same infinity-topos. | |
| Nov 27, 2014 at 18:12 | comment | added | Simon Henry | Thanks ! Do you know if there Is a counterexample without additional assumption ? | |
| Nov 27, 2014 at 18:10 | vote | accept | Simon Henry | ||
| Nov 27, 2014 at 17:42 | history | answered | David Carchedi | CC BY-SA 3.0 |