Timeline for Skeleton of a braided monoidal category
Current License: CC BY-SA 2.5
3 events
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| Jul 12, 2010 at 17:37 | history | edited | Benjamin Enriquez | CC BY-SA 2.5 |
improved presentation
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| Jul 12, 2010 at 15:50 | comment | added | Anton Kapustin | I think $\beta_{A,B}$ in general does not satisfy the hexagon axiom. Here is an example. Consider the category of Z-graded complex vector spaces, with the strict monoidal structure given by the convolution: $V_x\otimes V_y=V_{x+y}$. Let us define a nontrivial braiding $\beta(V_x,V_y)=\exp(a xy)$ for some complex number $a$. Now let $k$ be an integer and let's modify the category by introducing morphisms between vector spaces in degree $x$ and vector spaces in degree $x+k$, so that nonisomorphic objects live in the range $0\leq x\leq k-1$. For obvious choices of $p$ and $i$, the hexagon fails. | |
| Jul 12, 2010 at 6:38 | history | answered | Benjamin Enriquez | CC BY-SA 2.5 |