[Merged by Bors] - feat(category_theory/sites): sheaves on types #5259
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kckennylau
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Dec 6, 2020
kckennylau
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b-mehta
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src/category_theory/sites/types.lean
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| In this file we define a grothendieck topology on the category of types, | ||
| and construct the canonical function that sends a type to a sheaf over | ||
| the category of types. |
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Do you actually construct this function? I think a better description would be to say something like the yoneda presheaf for any type is a sheaf (or to actually make a function which takes types to sheaves).
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@kckennylau ⬆️ what do you think?
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Now I have actually constructed the functor and the induced equivalence of categories.
Co-authored-by: Bhavik Mehta <bhavikmehta8@gmail.com>
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src/category_theory/sites/types.lean
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| @@ -54,6 +54,11 @@ theorem is_sheaf_yoneda' {α : Type u} : is_sheaf types_grothendieck_topology (y | |||
| by { convert this, exact rfl }, | |||
| λ f hf, funext $ λ y, by convert congr_fun (hf _ (hs y)) punit.star⟩ | |||
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| /-- The yoneda functor that sends a type to a sheaf over the category of types -/ | |||
| def yoneda' : Type u ⥤ Sheaf types_grothendieck_topology := | |||
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Can you add @[simps] to this, and show that composing this with the forgetful functor Sheaf => Presheaf is yoneda?
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