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hom-functor [2014/06/26 14:30] nikolaj |
hom-functor [2014/06/26 14:30] nikolaj |
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| == More general cases == | == More general cases == | ||
| - Extending this to a category of non-commutative groups is a research subject. Tannakian categories ... Grothendieck stuff ... we see that it's desirable for the Hom-sets to have their own algebraic structure (in the above, the Hom-set was again a group) and this is where many ideas come from. | - Extending this to a category of non-commutative groups is a research subject. Tannakian categories ... Grothendieck stuff ... we see that it's desirable for the Hom-sets to have their own algebraic structure (in the above, the Hom-set was again a group) and this is where many ideas come from. | ||
| - | - A similar construction works if we consider commutative Banach algebra and their maps maps to $\mathbb C$. This is the Gelfand transform business. It reduces to the Fourier transform if we consdier the space $L^1(\mathbb R)$ and convolution as multiplication. | + | - A similar construction works if we consider commutative Banach algebra and their maps maps to $\mathbb C$. This is the Gelfand transform business. It reduces to the Fourier transform if we consider the space $L^1(\mathbb R)$ and convolution as multiplication. |
| === Yoneda === | === Yoneda === | ||
