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yoneda_embedding [2015/03/14 01:10] nikolaj |
yoneda_embedding [2015/03/14 01:13] nikolaj |
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$h\circ g : \mathrm{Hom}(X,A)$ ... $f\circ h\circ g : \mathrm{Hom}(X,B)$ | $h\circ g : \mathrm{Hom}(X,A)$ ... $f\circ h\circ g : \mathrm{Hom}(X,B)$ | ||
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+ | Note how the $\mathrm{Hom}$-functors themselves are contravariant, as seen by the direction of the vertical arrows: $g: X\to Y$ but e.g. the associated fmap goes from $\mathrm{Hom}(Y,A)$ to $\mathrm{Hom}(X,A)$. | ||
=== Yoneda lemma === | === Yoneda lemma === |