Timeline for Small objects in categories
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 4, 2014 at 13:02 | vote | accept | Marci | ||
| Jan 3, 2014 at 23:54 | comment | added | Qiaochu Yuan | "Point" can also mean "monoidal unit for some natural monoidal structure" (not necessarily the product or coproduct, as in the case of the terminal or initial object respectively). | |
| Jan 3, 2014 at 20:54 | comment | added | Dylan Wilson | I think the fact that we had the initial/final object was incidental. That a point is a compact generator is what we're after. In the category of chain complexes of $R$-modules you'd start with $R$; closing under finite homotopy colimits would give finite complexes of free modules. Again, idempotent completing gives perfect complexes. | |
| Jan 3, 2014 at 20:44 | comment | added | Marci | Thank you! My only problem is the following. Point in a general category should be either the initial object or the terminal object. In the category of $R$-mod or in the category of (co)chain complexes, however, it is the trivial object (0), and any colimit of that is the trivial object, so I won't get any interesting objects. | |
| Jan 3, 2014 at 20:31 | history | answered | Dylan Wilson | CC BY-SA 3.0 |