Timeline for What is the comultiplication of a matrix frobenius algebra?
Current License: CC BY-SA 2.5
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| Oct 31, 2009 at 23:38 | history | edited | Theo Johnson-Freyd | CC BY-SA 2.5 |
fixed a typo
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| Oct 29, 2009 at 12:37 | comment | added | Aleks Kissinger | This is a good way of thinking about these things! Also, it justifies the existence of what I previously thought was a cute but somewhat pointless construction of turning a compact structure (cap and cup) into a frobenius algebra. This is exactly the matrix frobenius algebra, when you think of linear maps as their "names". I.e. express M as "[M] := (1 (x) M) o cup". The frobenius multiplication "mu ([M] (x) [N])" reduces by compact structure "string pulling" to [MN]. Cool! Defining trace as cap also unifies the "internal" notion of trace of a matrix with the "self-loop" one: Tr(M) = cap[M]. | |
| Oct 27, 2009 at 20:59 | history | answered | Theo Johnson-Freyd | CC BY-SA 2.5 |