Timeline for Simplicial Objects in Additive Categories
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 22, 2019 at 17:14 | comment | added | Fernando Muro | The Yoneda embedding suffices. A simplicial object only involves countably many objects of the abelian category. | |
| Apr 21, 2019 at 21:03 | comment | added | Dmitri Pavlov | @S.carmeli: The Yoneda embedding only works for small additive categories. For large categories there is Adelman's embedding theorem. See mathoverflow.net/questions/52881/… | |
| Apr 21, 2019 at 19:55 | comment | added | S. carmeli | @FernandoMuro right! thats so simple yet so cool. And I guess the Yoneda embedding $\mathcal{A} \to Fun^{\oplus}(\mathcal{A}^{op},Ab)$ gives us such an embedding right? | |
| Apr 21, 2019 at 16:23 | comment | added | Fernando Muro | You just embed the additive category into an abelian category and you get the result you want. | |
| Apr 21, 2019 at 15:56 | vote | accept | S. carmeli | ||
| Apr 21, 2019 at 15:55 | comment | added | S. carmeli | Thanks for the references! My feeling is of course the same, that the formulas uses only addition and subtraction so you should not need kernels an cokernels, but I hoped that it is stated in this language somewhere. If not, I guess varifying it myself in the text is the only option :-) | |
| Apr 21, 2019 at 15:19 | history | answered | Dmitri Pavlov | CC BY-SA 4.0 |