Timeline for Does formation of the derived $\infty$-category preserve pushouts?
Current License: CC BY-SA 4.0
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| Aug 30, 2020 at 14:51 | comment | added | Dylan Wilson | @Stahl you can identify objects of $\mathsf{Mod}_B \otimes_{\mathsf{Mod}_A}\mathsf{Mod}_C$ with $B$-$C$-bimodule objects in the category of $A$-modules. Is that more along the lines of what you were looking for? (This is a special case of HA.4.8.4.6). | |
| Aug 30, 2020 at 8:11 | comment | added | Stahl | Thanks Dylan, this is very helpful! While this certainly answers my question, I must admit I was hoping for something like being able to explicitly show that every module over $B\otimes_A C$ is equivalent in some homotopy appropriate sense to a "compatible pair" $(M,N)\in\operatorname{Mod}_{B}\times\operatorname{Mod}_{C}.$ Maybe this is as hands-on as it gets in the $\infty$-category world, though... | |
| Aug 30, 2020 at 8:06 | vote | accept | Stahl | ||
| Aug 27, 2020 at 12:18 | history | answered | Dylan Wilson | CC BY-SA 4.0 |