feat(Algebra): exact of associated graded exact

[Thmoas-Guan]

We proved that a chain complex is exact if its associated graded complex is exact.

Co-authored-by: Huanyu Zheng @Yu-Misaka [email protected] Co-authored-by: Yi Yuan @yuanyi-350 [email protected] Co-authored-by: Weichen Jiao @AlbertJ-314 [email protected]

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• [ ] depends on: #26868

migrated from #22972

[github-actions[bot]]

PR summary 16dc83e76d

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.RingTheory.FilteredAlgebra.AssociatedGraded (new file)	533
Mathlib.RingTheory.FilteredAlgebra.FilteredHom (new file)	534
Mathlib.RingTheory.FilteredAlgebra.Exactness (new file)	797

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Declarations diff

+ AssociatedGraded + AssociatedGradedAddMonoidHom + AssociatedGradedAddMonoidHom_apply + AssociatedGradedAddMonoidHom_apply_of + AssociatedGradedAddMonoidHom_comp_eq_comp + AssociatedGradedAddMonoidHom_exact_of_GradedPieceHom_exact + FilteredAddGroupHom + FilteredHom + FilteredHomClass + GradedPiece + GradedPieceHom + GradedPieceHom_apply_mk_eq_mk_piece_wise_hom + GradedPieceHom_comp + GradedPieceHom_comp_apply + GradedPieceHom_exact_of_AssociatedGradedAddMonoidHom_exact + IsDiscreteFiltration + IsExhaustiveFiltration + IsStrict + IsStrict.strict + IsStrict.strict_lt + IsStrict_of_Int + associatedGraded_of_mem_ker_iff + associatedGraded_of_mem_range_iff + exact_component_of_strict_exact_component + exact_of_strict_exact + ext + induction_on + instance : AddMonoidHomClass (FilteredAddGroupHom FA FA_lt FB FB_lt) A B + instance : Coe (FilteredAddGroupHom FA FA_lt FB FB_lt) (FilteredHom FA FA_lt FB FB_lt) + instance : FilteredHomClass (FilteredAddGroupHom FA FA_lt FB FB_lt) FA FA_lt FB FB_lt + instance : FilteredHomClass (FilteredHom FA FA_lt FB FB_lt) FA FA_lt FB FB_lt + instance : FunLike (FilteredAddGroupHom FA FA_lt FB FB_lt) A B + instance : FunLike (FilteredHom FA FA_lt FB FB_lt) A B + instance [Preorder ι] [IsFiltration F F_lt] (i : ι) : Setoid (AddSubgroup.ofClass (F i)) + ker_in_range_of_graded_exact + mem_ker_iff + mem_range_iff + mk_apply_of_mem + mk_apply_of_not_mem + mk_eq + mk_injective + mk_piece_wise + of + of_apply + of_eq_of_ne + of_eq_self + of_injective + strict_of_exact_discrete + strict_of_exhaustive_exact + sum_support_of + sum_univ_of + support_of + support_of_subset + zero_of_pieces_range ++ comp ++ id ++ mk ++ piece_wise_hom

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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Increase in tech debt: (relative, absolute) = (1.00, 0.06)

Current number	Change	Type
18	1	disabled simpNF lints

Current commit 6806b3278a Reference commit 16dc83e76d

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• leanprover-community/mathlib4#26868 By Dependent Issues (🤖). Happy coding!

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[Thmoas-Guan]

I handed this PR out to another collaborator, the new PR is #33227.