Timeline for Compact Generation of Co-Module Categories
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 5, 2020 at 13:54 | comment | added | Saal Hardali | In this generality it is certainly false. Let $C$ be the coaugmented counital coalgebra over $\mathbb{Q}$ cogenerated by a single primitive cogenerator in (homological) degree $3$. Then $\pi_{\ast} (Comod_C(\mathbb{Q})) = \mathbb{Q}[x]$ with $|x| = 2$ so $\mathbb{Q}$ can't be compact because then $\mathbb{Q}[x^{-1}] = 0$ contradicting that $\pi_{\ast} (End_C(\mathbb{Q}))[x^{-1}] = \mathbb{Q}[x,x^{-1}] \ne 0$ | |
| Feb 13, 2019 at 9:16 | comment | added | Saal Hardali | Aha, this is the one I know how to make sense of in this generality. Notice however that there are other useful variants which do not always agree see arxiv.org/abs/0905.2621 | |
| Feb 13, 2019 at 9:00 | comment | added | Gal Dor | Opposite category of the category of modules in the opposite category of $\mathcal{C}$. | |
| Feb 13, 2019 at 8:32 | comment | added | Saal Hardali | Probably a stupid question but what definition of the $\infty$ category of comodules are you using? | |
| Feb 13, 2019 at 8:15 | history | asked | Gal Dor | CC BY-SA 4.0 |