Timeline for About a zig-zag of Quillen adjunctions
Current License: CC BY-SA 4.0
6 events
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| Sep 12, 2018 at 13:31 | history | edited | Philippe Gaucher | CC BY-SA 4.0 |
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| Sep 12, 2018 at 13:29 | comment | added | Philippe Gaucher | @DavidWhite Unfortunately, I think that I cannot avoid to understand $L_1$ for which I don't know any explicit form. I just know that $L_1$ exists thanks to the theory of locally presentable categories. I wonder whether there is a characterization of a Quillen equivalence $L\dashv R$ which only uses $L$ or which only uses $R$; I am not aware of such a statement. All characterizations I know use both $L$ and $R$. | |
| Sep 12, 2018 at 1:08 | history | edited | Philippe Gaucher | CC BY-SA 4.0 |
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| Sep 11, 2018 at 16:40 | comment | added | David White | I'm just between classes, with no time for a real answer, but an observation: the Quillen adjunction $(L_1,R_1)$ is a Quillen equivalence if and only if, on the level of homotopy categories, it induces an equivalence of categories. The hypothesis in (4) says that those homotopy categories are indeed equivalent (because $(L_2,R_2)$ also induces an equivalence of homotopy categories by (3)), so it's at least plausible. | |
| Sep 11, 2018 at 13:43 | history | edited | Philippe Gaucher | CC BY-SA 4.0 |
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| Sep 11, 2018 at 13:27 | history | asked | Philippe Gaucher | CC BY-SA 4.0 |