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The Structure Sheaf #941

Merged
merged 46 commits into from
Oct 14, 2022
Merged

The Structure Sheaf #941

merged 46 commits into from
Oct 14, 2022

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mzeuner
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@mzeuner mzeuner commented Oct 10, 2022

In this PR we construct the structure sheaf on the Zariski lattice of a commutative ring and prove the sheaf property.
This builds on #929 but diverges a bit, so it might be best to close that PR.

The older and weaker "pullback" version can probably be removed now.

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Great stuff! Some minor suggestions, discussed IRL

open CommRingStr
private
A = fst Aφ
froToCommRingPath : CommAlgebra→CommRing (toCommAlg Aφ) ≡ fst Aφ
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Not a great name and also in another PR?

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fst Aφ is just A

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Yeah something similar is done in #931

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Did you decide what to do about this? Maybe just a better name is sufficient?

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I went with CommAlgebra→CommRing≡

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Maybe @MatthiasHu can fix his PR once this is merged and figure out what broke in his proposal

Cubical/Algebra/ZariskiLattice/Base.agda Show resolved Hide resolved
Cubical/Algebra/ZariskiLattice/Base.agda Show resolved Hide resolved
Cubical/Algebra/ZariskiLattice/StructureSheafPullback.agda Outdated Show resolved Hide resolved
Cubical/Categories/Instances/CommAlgebras.agda Outdated Show resolved Hide resolved
Cubical/Algebra/ZariskiLattice/StructureSheaf.agda Outdated Show resolved Hide resolved
Cubical/Algebra/ZariskiLattice/StructureSheaf.agda Outdated Show resolved Hide resolved
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@mzeuner
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mzeuner commented Oct 14, 2022

OK, hope the checks pass and the PR is ready to merge now.

@mortberg mortberg merged commit 17edc77 into agda:master Oct 14, 2022
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2 participants