Timeline for answer to Freyd-Mitchell for $k$-linear categories by user144185
Current License: CC BY-SA 4.0
Post Revisions
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 22, 2020 at 14:11 | vote | accept | 57Jimmy | ||
| Apr 22, 2020 at 11:29 | comment | added | user144185 | @JeremyRickard thank you! I edited the answer and I think that now it is right. | |
| Apr 22, 2020 at 11:27 | history | edited | user144185 | CC BY-SA 4.0 |
added 492 characters in body
|
| Apr 22, 2020 at 9:27 | comment | added | Jeremy Rickard | I agree with the conclusion that $R$ can be taken to be a $k$-algebra, with the embedding $k$-linear. But this is not how the Freyd-Mitchell embedding is constructed. Firstly, your construction embeds $\mathcal{A}$ into $\mathcal{L}(\mathcal{A}^{\text{op}},\operatorname{Ab})$, not $\mathcal{L}(\mathcal{A},\operatorname{Ab})$. And also, it is not true in general that $\mathcal{L}(\mathcal{A},\operatorname{Ab})$ has a projective generator. But it does have an injective cogenerator, which is what is used to construct the Freyd-Mitchell embedding. | |
| Apr 22, 2020 at 1:47 | history | edited | user144185 | CC BY-SA 4.0 |
deleted 50 characters in body
|
| Apr 21, 2020 at 22:53 | history | edited | LSpice | CC BY-SA 4.0 |
Link to book; proofreading and TeX
|
| Apr 21, 2020 at 22:38 | history | edited | user144185 | CC BY-SA 4.0 |
deleted 14 characters in body
|
| Apr 21, 2020 at 22:19 | history | answered | user144185 | CC BY-SA 4.0 |