Timeline for The single-plus construction is not the left adjoint of the inclusion of separated presheaves?
Current License: CC BY-SA 2.5
4 events
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| Dec 22, 2010 at 5:16 | comment | added | Mike Shulman | The plus construction seems very intuitive to me: to make F into a sheaf, you want the sections of F over U to be determined by matching families over covers of U, so you simply replace F(U) by the set of all such matching families, modulo the obvious equivalence relation. It's maybe a little naive, but it's natural. It converges after 2 steps because sets are discrete; for stacks you need 3 steps, and for ∞-stacks you need transfinite steps. You can also think of it as a version of the small object argument, with sheaves as the fibrant objects. | |
| Dec 15, 2010 at 9:12 | comment | added | Angelo | Well, it seems to me that I am the wrong person to ask. Anyway, I share your feelings about the plus construction. | |
| Dec 15, 2010 at 8:03 | comment | added | Harry Gindi | Thanks! I've got a quick question for you, then! Why are your notes the only place that I can find the construction $(-)^{sep}$? The double-plus construction seems pretty unintuitive, and the fact that it works seems more like a coincidence than anything. | |
| Dec 15, 2010 at 7:20 | history | answered | Angelo | CC BY-SA 2.5 |