Timeline for "Approximating" functors by Hom/Tensor product
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 29, 2022 at 20:35 | comment | added | Maxime Ramzi | First, contravariantly it is never an equivalence except in trivial cases - this is because a category cannot be presentable and have its opposite be presentable too without being a preorder or something. Second, your statement in classical Morita theory is wrong (think about $A= B = \mathbb Z, X= \mathbb Z^n$), you need this condition + something about endomorphism rings. The same kind of criterion holds in this $\infty$-word by replacing "finitely generated projective" with "compact" or equivalently "perfect" | |
| Mar 29, 2022 at 19:00 | comment | added | curious math guy | Can I ask a follow-ups? In the "classical" Morita theory, we know that $-\otimes X$ is an equivalence iff $X$ is a finitely generated projective generator (when view as $A$ and $B$-module respectively). Do we have a similar criterion here in the stable-infinity case and contravariantly? | |
| Mar 29, 2022 at 16:27 | comment | added | curious math guy | I think this is a wonderful answer, thanks! | |
| Mar 29, 2022 at 16:26 | vote | accept | curious math guy | ||
| Mar 29, 2022 at 14:30 | history | answered | Maxime Ramzi | CC BY-SA 4.0 |