Timeline for Descent of Morphisms of Sheaves
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 27, 2012 at 21:01 | comment | added | cheyne | My notation was correct, my statement had a major typo in it: I meant to go from Sh(Y) to Sh(W). | |
| May 27, 2012 at 20:59 | history | edited | cheyne | CC BY-SA 3.0 |
edited body
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| May 10, 2012 at 20:07 | vote | accept | cheyne | ||
| May 10, 2012 at 20:00 | comment | added | Zhen Lin | @Cheyne: Your notation is bad. The functor from $\textbf{Sh}(W)$ to $\textbf{Sh}(Z)$ should be denoted $h_*$, etc. The notation $h^{-1}$ (or $h^*$) is reserved for the one going in the opposite direction. And it is true that this "inverse image" functor does not compose strictly: $h^{-1} g^{-1} \ne (g \circ h)^{-1}$. There is, however, a natural isomorphism. | |
| May 10, 2012 at 13:46 | answer | added | Moshe | timeline score: 3 | |
| May 10, 2012 at 13:05 | history | edited | cheyne | CC BY-SA 3.0 |
Reformulated questions, and more clearly defined my terms in the beginning.
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| May 10, 2012 at 12:53 | comment | added | cheyne | @David Above is the "new" definition for a presheaf, which is all I am concerned about at the moment. I will be more clear now. @Martin: Turns out the book is using all of this exposition to define a stack in this context, hence why I am unfamiliar with it up to this point. | |
| May 9, 2012 at 23:42 | comment | added | David Carchedi | If you want anyone to attempt to answer this question, I suggest you say what this "new" definition of a sheaf is. | |
| May 9, 2012 at 22:38 | comment | added | cheyne | No, to be honest, I am really trying to do this all without talking about stacks (or schemes, etc). The goal is to define these descent properties in a "hands-on" way so that I can understand the definition of a "gerbe" in a "hands-on" way. | |
| May 9, 2012 at 21:21 | comment | added | Martin Brandenburg | First; are you aware of the notions of pseudo-functors and stacks? | |
| May 9, 2012 at 21:12 | history | asked | cheyne | CC BY-SA 3.0 |