Timeline for Is every "nice" abelian category with enough projectives an additive presheaf category?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 8, 2018 at 16:56 | vote | accept | Tim Campion | ||
| Jan 8, 2018 at 17:00 | |||||
| Jan 8, 2018 at 0:49 | comment | added | Tim Campion | Darn, you're right. I suppose I asked the wrong question after all. | |
| Jan 7, 2018 at 23:57 | comment | added | Qiaochu Yuan | I would rather just think about $\text{Ab}$-enriched categories directly as a generalization of rings (they are "rings with many objects," or "ringoids" if you really want). | |
| Jan 7, 2018 at 22:07 | comment | added | Benjamin Steinberg | This is a module category if you are willing to loosen your definition of rings from unital rings to rings with local units. A ring R has local units if it is a direct limit of unital rings via homomorphisms that are not necessarily unit preserving. The category of unitary R-modules consists of those modules M with RM=M. If C is a category the category algebra ZC has local units ands its unitary modules are just the functors on C to Ab (up to equivalence of categories). | |
| Jan 7, 2018 at 19:49 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |