feat(Algebra/Homology): connecting a chain complex and a cochain complex

[joelriou]

Given a chain complex K: ... ⟶ K.X 2 ⟶ K.X 1 ⟶ K.X 0, a cochain complex L: L.X 0 ⟶ L.X 1 ⟶ L.X 2 ⟶ ..., a morphism d₀: K.X 0 ⟶ L.X 0 satisfying the identifies K.d 1 0 ≫ d₀ = 0 and d₀ ≫ L.d 0 1 = 0, we construct a cochain complex indexed by ℤ of the form ... ⟶ K.X 2 ⟶ K.X 1 ⟶ K.X 0 ⟶ L.X 0 ⟶ L.X 1 ⟶ L.X 2 ⟶ ..., where K.X 0 lies in degree -1 and K.X 0 in degree 0.

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[github-actions]

PR summary c56b85d8b5

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Algebra.Homology.Embedding.Connect (new file)	666

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Declarations diff

+ ConnectData
+ X
+ X_negOne
+ X_negSucc
+ X_ofNat
+ X_zero
+ cochainComplex
+ d
+ d_comp_d
+ d_negSucc
+ d_ofNat
+ d_sub_one_zero
+ d_sub_two_sub_one
+ d_zero_one
+ shape

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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No changes to technical debt.

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).

[callesonne]

Straightforward, LGTM!