Timeline for Nomenclature question: a morita-invariant way to say finite-dimensional?
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5 events
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| Sep 19, 2016 at 15:51 | comment | added | A K | In the second situation, I thought that $A$ is $k$-dg-algebra, and you are looking for something analogous and by "$\text{hom}(P, M)$ is finite-dimensional in finitely-many homological degrees" again mean that it has cohomology which is finite-dimensional over $k$. | |
| Sep 19, 2016 at 15:36 | comment | added | A K | What do you mean by "$\text{Hom}(P, M)$ is finite-dimensional" in the first situation? I thought that it is the dimension of this module over $k$. Indeed $M \in \mathcal{C}$ is finite-dimensional over $k$ if and only if $\text{Hom}(P, M)$ is finite-dimensional as $k$-module. | |
| Sep 19, 2016 at 15:16 | comment | added | Dmitry Vaintrob | No, I don't think that's it: in order to be able to talk about a $\mathfrak{C}$-module as a $k$-module, you need some sort of fiber functor $\mathfrak{C}\to \text{vect}$, which I'm assuming isn't given. | |
| Sep 19, 2016 at 2:23 | review | First posts | |||
| Sep 19, 2016 at 2:24 | |||||
| Sep 19, 2016 at 2:22 | history | answered | A K | CC BY-SA 3.0 |