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Cohomology Rings #759

Merged
merged 91 commits into from
May 7, 2022
Merged

Cohomology Rings #759

merged 91 commits into from
May 7, 2022

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thomas-lamiaux
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Add a proper definition of the cohomology rings.

Work in progress : compute some cohomology rings

thomas-lamiaux and others added 17 commits April 6, 2022 13:57
The index and the groups were at the same level.
The should be at different one, for instance if the index is Nat, and the group something else
-> Modify some notions in gradedCommutativity
-> new lemme for the "good" -h^
-> proof
-> Because this case is so degenerated, things compute.
   This new proof is forgetting some of the computation
   to have proof that will rise better to non-degenerated case
-> changing gradedComm by gradedCom' to account
   the previuous change
@thomas-lamiaux
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To prove that H^n (X) are gradedCommutative, -h _ . _ is introduced.
However it is not introduced using -_h but by new direct definition to have more specific computations rules.

Hence I have a introduced a -h _ ._ and renamed the other one and the related function by adding a prime.
Prove that it is equal, and added a proof of gradedComm for the "good" -h _ . _
This enables to rise it more easily to the cohomology ring H*(X)

Nevertheless, this breaks a lot of dependency because the graded operator is used in several files.
Yet I do believe that it is for the the best, as it described more accurately what is done.
Plus, it suffices to add a ' to the dependent files to fix the issue, one must just find them all.

@thomas-lamiaux
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The content of the Pull request is done.
The only thing left to do is some clean up and standardization of the files

@thomas-lamiaux thomas-lamiaux marked this pull request as ready for review May 5, 2022 22:03
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@mortberg mortberg merged commit 4edc600 into agda:master May 7, 2022
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2 participants