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[Merged by Bors] - feature(algebraic_geometry/Scheme): the category of schemes #3961
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Co-authored-by: Markus Himmel <markus@himmel-villmar.de>
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| @[ext] lemma ext {X Y : PresheafedSpace C} (α β : hom X Y) | ||
| (w : α.base = β.base) (h : α.c ≫ (whisker_right (nat_trans.op (opens.map_iso _ _ w).inv) X.𝒪) = β.c) : | ||
| (w : α.base = β.base) | ||
| (h : α.c ≫ (whisker_right (nat_trans.op (opens.map_iso _ _ w).inv) X.presheaf) = β.c) : |
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Is this the solution to the problem of equality of types?
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I'm sorry, could you clarify your question, I'm not sure how it relates to this piece of the code.
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Well, equality of types proved to be troublesome, but somehow you managed to use it without issues. (α.base = β.base is an equality of types right)
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| /-- The structure sheaf of a locally ringed space. -/ | ||
| def 𝒪 : sheaf CommRing X.to_Top := ⟨X.1.presheaf, X.1.sheaf_condition⟩ |
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Why not coerce X to a sheafed space?
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I can't do exactly that, but I've replaced the RHS with X.to_SheafedSpace.sheaf. Is that okay?
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Sure, but why do we not prefer coercion?
Co-authored-by: Kenny Lau <kc_kennylau@yahoo.com.hk>
Co-authored-by: Kenny Lau <kc_kennylau@yahoo.com.hk>
Co-authored-by: Bryan Gin-ge Chen <bryangingechen@gmail.com>
Co-authored-by: Bryan Gin-ge Chen <bryangingechen@gmail.com>
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The definition of a `Scheme`, and the category of schemes as the full subcategory of locally ringed spaces. Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Ashvni <ashvni.n@gmail.com>
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The definition of a `Scheme`, and the category of schemes as the full subcategory of locally ringed spaces. Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Ashvni <ashvni.n@gmail.com>
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The definition of a `Scheme`, and the category of schemes as the full subcategory of locally ringed spaces. Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Ashvni <ashvni.n@gmail.com>
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The definition of a
Scheme, and the category of schemes as the full subcategory of locally ringed spaces.Co-authored-by: Johan Commelin johan@commelin.net
Blocked
#3609,#3906,#3907