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If C has finite products then representables are tiny ([よ(t), —] has an amazing right adjoint)
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| [よ(t), X] ⇒ Y | |
| = ∀ d. (よ(t) × よ(d) ⇒ X) → Y(d) | |
| = ∀ d. (よ(t × c) ⇒ X) → Y(d) | |
| = ∀ d. X(t × d) → Y(d) | |
| = ∀ d c. X(c) → (t × d → c) → Y(d) | |
| = ∀ c. X(c) → ∀ d. (t × d → c) → Y(d) | |
| = ∀ c. X(c) → ∀ d. (よ(t) × よ(d) ⇒ よ(c)) → Y(d) | |
| = ∀ c. X(c) → ([よ(t), よ(c)] ⇒ Y) | |
| = X ⇒ √Y |
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