Timeline for Are there any nontrivial abelian categories with only finitely many objects?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Nov 12, 2012 at 21:41 | vote | accept | user27976 | ||
| Nov 10, 2012 at 14:33 | answer | added | Jeremy Rickard | timeline score: 58 | |
| Nov 10, 2012 at 14:10 | comment | added | François Brunault | Considering the multiplication by $p$ on the nonzero object with $p$ prime, it seems the base ring $R$ of the hypothetical special module can be taken to be either a $\mathbf{Z}/p\mathbf{Z}$ algebra or a $\mathbf{Q}$-algebra. | |
| Nov 10, 2012 at 8:26 | comment | added | Zhen Lin | If there is an abelian category $\mathcal{C}$ with only one non-zero object $A$, then its endomorphism ring must fail to have the invariant basis number property: because then $\mathcal{C}(A, A) \cong \mathcal{C}(A, A \times A) \cong \mathcal{C}(A, A) \times \mathcal{C}(A, A)$ as right $\mathcal{C}(A, A)$-modules. | |
| Nov 10, 2012 at 6:34 | history | edited | Eric Wofsey | CC BY-SA 3.0 |
edited title
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| Nov 10, 2012 at 5:58 | history | asked | user27976 | CC BY-SA 3.0 |