Timeline for Twisted duality in a symmetric monoidal category
Current License: CC BY-SA 3.0
3 events
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| Feb 4, 2013 at 14:50 | comment | added | Martin Brandenburg | Up to now I only have boring examples where $L$ is not invertible. 1) If $\mathcal{C}$ is discrete, then $L=X \otimes Y$ always works. 2) More generally $L=X \otimes Y$ (with the obvious morphisms) works if $X$ and $Y$ are symtrivial (mathoverflow.net/questions/119689). For example $\mathbb{Q} \otimes_{\mathbb{Z}} \mathbb{Q} \to \mathbb{Q}$ is a perfect pairing of $\mathbb{Z}$-modules. 3) If $\mathcal{C}$ is additive and $L= 1^{\oplus I}$ for a finite set $I$, then $X$ is dual to $Y$ twisted by $L$ iff for every $i \in I$ we have a duality between $X$ and $Y$ and these are "orthogonal". | |
| Feb 4, 2013 at 13:55 | comment | added | S. Carnahan♦ | Do you have any examples where the twisting object is not invertible? The notions of dualizing object and Serre functor are well-established, but as far as I know, they are limited to the invertible case. | |
| Feb 4, 2013 at 11:55 | history | asked | Martin Brandenburg | CC BY-SA 3.0 |