Timeline for Idempotent completion of linear categories and Yoneda
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Mar 28, 2019 at 13:46 | history | edited | Arthur | CC BY-SA 4.0 |
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| Mar 28, 2019 at 13:18 | history | edited | Arthur | CC BY-SA 4.0 |
added 35 characters in body
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| Mar 27, 2019 at 23:30 | comment | added | Arthur | The question was badly formulated, I have edited it appropriately. | |
| Mar 27, 2019 at 23:13 | history | edited | Arthur | CC BY-SA 4.0 |
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| Mar 27, 2019 at 22:56 | history | edited | Arthur | CC BY-SA 4.0 |
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| Mar 27, 2019 at 20:53 | answer | added | Qiaochu Yuan | timeline score: 3 | |
| Mar 27, 2019 at 20:24 | comment | added | Qiaochu Yuan | Explicitly, if $C = \text{Vect}$, consider the presheaf $V \mapsto V^{\ast} \otimes W$ for infinite-dimensional $W$. This corresponds to linear maps $V \to W$ of finite rank, and it is not a direct summand of a representable presheaf, e.g. because it does not send colimits to limits. So semisimplicity does not suffice. It's also easy to construct counterexamples if you don't require your presheaves to be linear, which you don't specify in your question. | |
| Mar 27, 2019 at 19:08 | comment | added | Qiaochu Yuan | This should almost never hold, and it certainly does not suffice to assume semisimplicity. Are you sure this is the question you meant to ask? | |
| Mar 27, 2019 at 17:25 | review | First posts | |||
| Mar 27, 2019 at 17:26 | |||||
| Mar 27, 2019 at 17:22 | history | asked | Arthur | CC BY-SA 4.0 |