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space_and_quantity [2015/02/26 13:23] nikolaj |
space_and_quantity [2015/04/20 19:59] nikolaj |
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| Therefore, the topos ${\bf{Set}}^{\bf{C}^{op}}$ contains a copy of ${\bf{C}}$. | Therefore, the topos ${\bf{Set}}^{\bf{C}^{op}}$ contains a copy of ${\bf{C}}$. | ||
| - | See the idea discussion in [[Functor category]]. | + | Please also see the idea discussion in [[Functor category]]. |
| {{ hom_r_m_.png?X400}} | {{ hom_r_m_.png?X400}} | ||
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| === Quantity (Isbell adjunction) === | === Quantity (Isbell adjunction) === | ||
| - | The co-Yoneda (for presheaves $X\in{\bf{Set}}^{\bf{C}^{op}}$) lemma and the Yoneda lemma (for functors $F\in{\bf{Set}}^{\bf{C}}$$) tell us that | + | The co-Yoneda (for presheaves $X\in{\bf{Set}}^{\bf{C}^{op}}$) lemma and the Yoneda lemma (for functors $F\in{\bf{Set}}^{\bf{C}}$) tell us that |
| * $\mathrm{nat}(\mathrm{Hom}_{\bf{C}}(-,U),X)\cong XU=:{\mathrm{eval}}(X)U$ | * $\mathrm{nat}(\mathrm{Hom}_{\bf{C}}(-,U),X)\cong XU=:{\mathrm{eval}}(X)U$ | ||
