feat(Algebra/Homology): API for the homology of an extension of homological complexe

[joelriou]

Given an embedding e : c.Embedding c' of complex shapes, we provide definitions and lemmas in order to study the extension by e of a homological complex.

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• depends on: feat(Algebra/Homology): the left homology of an extension of homological complexes #18502
• depends on: feat(Algebra/Homology): the homology of an extension of homological complexes #19198

[github-actions]

PR summary 9e52c3cffd

Import changes exceeding 2%

%	File
+35.35%	Mathlib.Algebra.Homology.Embedding.Extend

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Algebra.Homology.Embedding.Extend	727	984	+257 (+35.35%)

Import changes for all files

Files	Import difference
Mathlib.Algebra.Homology.Embedding.TruncGE	3
Mathlib.Algebra.Homology.Embedding.HomEquiv Mathlib.Algebra.Homology.Embedding.Extend	257
Mathlib.Algebra.Homology.Embedding.ExtendHomology	993

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Declarations diff

+ CokernelCofork.isColimitOfIsColimitOfIff
+ CokernelCofork.isColimitOfIsColimitOfIff'
+ KernelFork.isLimitOfIsLimitOfIff
+ KernelFork.isLimitOfIsLimitOfIff'
+ comp_d_eq_zero_iff
+ d_comp_desc_eq_zero_iff
+ d_comp_desc_eq_zero_iff'
+ d_comp_eq_zero_iff
+ extendCyclesIso
+ extendCyclesIso_hom_iCycles
+ extendCyclesIso_hom_naturality
+ extendCyclesIso_inv_iCycles
+ extendHomologyIso
+ extendHomologyIso_hom_homologyι
+ extendHomologyIso_hom_naturality
+ extendHomologyIso_inv_homologyι
+ extendOpcyclesIso
+ extend_exactAt
+ extend_exactAt_iff
+ hasHomology
+ homologyData
+ homologyData'
+ homologyπ_extendHomologyIso_hom
+ homologyπ_extendHomologyIso_inv
+ instance (j : ι) [K.HasHomology j] : (K.extend e).HasHomology (e.f j)
+ instance : (K.extend e).IsStrictlySupported e
+ instance [∀ j, K.HasHomology j] (j' : ι') : (K.extend e).HasHomology j' := by
+ leftHomologyData
+ lift_d_comp_eq_zero_iff
+ lift_d_comp_eq_zero_iff'
+ pOpcycles_extendOpcyclesIso_hom
+ pOpcycles_extendOpcyclesIso_inv
+ quasiIsoAt_extendMap_iff
+ quasiIso_extendMap_iff
+ rightHomologyData
++ cokernelCofork
++ isColimitCokernelCofork
++ isLimitKernelFork
++ kernelFork

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) = (6.00, 0.00)

Current number	Change	Type
1559	6	erw

Current commit 9e52c3cffd
Reference commit 66df24a8e2

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:

• feat(Algebra/Homology): the left homology of an extension of homological complexes #18502
• feat(Algebra/Homology): the homology of an extension of homological complexes #19198
  By Dependent Issues (🤖). Happy coding!