Timeline for Ind-objects in a coherent category
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 5, 2012 at 13:23 | comment | added | Buschi Sergio | From Sheaves in geometry and logic - MAc LAne MOerdijk, these are exatly the flat presheaves (see p. 386) (if $C$ is small) | |
| May 4, 2012 at 17:59 | comment | added | Ali Lahijani | Thanks Buschi, that is helpful but additionally I want to know what kind of diagrams they correspond to. Is there any relation with the diagram being flat as a functor $J^{op} \to C^{op}$ or something like that? | |
| May 4, 2012 at 12:15 | comment | added | Buschi Sergio | $Ind(C)$ is equivalent to the full subcategory $A\subset C^>$ of presheaves F such that the comma category $C\downarrow F$ is filtrant and with a final set of objects. (see S. Mardešić, J. Segal, Shape theory, North Holland 1982.) | |
| May 4, 2012 at 12:04 | comment | added | Buschi Sergio | $Ind(C)$ is equivalent to the left exact presheaves (with a genrating set on its comma categy) if $C$ has finite limits. | |
| May 4, 2012 at 9:07 | comment | added | Harry | Maybe Chapter 4 of Deligne's paper "le groupe fondamental de la droite projective moins trois points" might help. See math.ias.edu/files/deligne/GaloisGroups.pdf | |
| May 4, 2012 at 8:58 | history | asked | Ali Lahijani | CC BY-SA 3.0 |