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space_and_quantity [2015/02/26 13:24]
nikolaj
space_and_quantity [2015/04/20 19:59] (current)
nikolaj
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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
  
   * $\mathrm{nat}(\mathrm{Hom}_{\bf{C}}(-,​U),​X)\cong XU=:​{\mathrm{eval}}(X)U$   * $\mathrm{nat}(\mathrm{Hom}_{\bf{C}}(-,​U),​X)\cong XU=:​{\mathrm{eval}}(X)U$
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