Timeline for Are there examples where one proves something about the functor represented by an object using the functor it corepresents?
Current License: CC BY-SA 2.5
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| Apr 24, 2010 at 21:53 | comment | added | JBorger | Actually, here's something for abstract groups. Being abelian is a good Yoneda property ($G$ is abelian if and only if every map from the free group $F_2$ factors through the quotient $\mathbf{Z}^2$). Then a finite group is abelian if and only if every irreducible complex representation is 1-dimensional. (BTW, how necessary is the finiteness assumption here?) | |
| Apr 24, 2010 at 21:50 | comment | added | JBorger | That's pretty good. It would be nice to carry it a bit further and find a nice example where some property of the functor $\mathrm{Hom}(-,G)$ is established by studying its representations. Here $G$ is the absolute Galois group. | |
| Apr 24, 2010 at 16:40 | history | answered | S. Carnahan♦ | CC BY-SA 2.5 |