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feat(CategoryTheory/Abelian): construction of reduced left resolutions#22547

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feat(CategoryTheory/Abelian): construction of reduced left resolutions#22547
joelriou wants to merge 15 commits intomasterfrom
jriou-left-resolution-reduced

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@joelriou joelriou commented Mar 4, 2025

The standard functorial free resolution of a R-module M does not directly extend to free resolutions of (bounded above) complexes because the free R-module functor does preserve zero morphisms. In this PR, we provide a general construction which takes functorial left resolutions and modify them by considering a suitable direct factor so that it preserves zero morphisms.


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@joelriou joelriou added the t-category-theory Category theory label Mar 4, 2025
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github-actions bot commented Mar 4, 2025

PR summary 8a246bcb1c

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.Algebra.Homology.LeftResolutions.Basic (new file) 988
Mathlib.Algebra.Homology.LeftResolutions.Transport (new file) 989
Mathlib.Algebra.Homology.LeftResolutions.Reduced (new file) 994

Declarations diff

+ Karoubi.retract
+ LeftResolutions
+ chainComplex
+ chainComplexFunctor
+ chainComplexMap
+ chainComplexMap_comp
+ chainComplexMap_f_0
+ chainComplexMap_f_1
+ chainComplexMap_f_succ_succ
+ chainComplexMap_id
+ chainComplexMap_zero
+ chainComplexXIso
+ chainComplexXOneIso
+ chainComplexXZeroIso
+ cokernel.map_id
+ cokernel.map_zero
+ exactAt_map_chainComplex_succ
+ instance (X : A) : Epi ((karoubi.π Λ).app ((toKaroubi _).obj X)) := by
+ instance (X : A) : Epi ((karoubi.π' Λ).app X) := by
+ instance (X : Karoubi A) : Epi ((karoubi.π Λ).app X)
+ instance : (karoubi.F Λ).PreservesZeroMorphisms
+ instance : (toKaroubi C).PreservesEpimorphisms
+ instance : (toKaroubi C).PreservesMonomorphisms
+ instance : Λ.karoubi.F.PreservesZeroMorphisms
+ instance : Λ.reduced.F.PreservesZeroMorphisms := by
+ karoubi
+ karoubi.F
+ karoubi.F'
+ karoubi.π
+ karoubi.π'
+ karoubi.π_app_toKaroubi_obj
+ kernel.map_id
+ kernel.map_zero
+ map_chainComplex_d
+ map_chainComplex_d_1_0
+ mk'XIso
+ mk'_congr_succ'_d
+ mk'_d
+ mkAux_eq_shortComplex_mk_d_comp_d
+ mkXIso
+ mk_congr_succ_X₃
+ mk_congr_succ_d₂
+ mk_d
+ ofCompIso
+ reduced
+ retractArrowApp
+ transport
+ whiskeringLeftObjToKaroubiFullyFaithful
+ π_naturality
- mk'_X_succ
- mk'_d_succ

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.


Decrease in tech debt: (relative, absolute) = (0.19, 0.00)
Current number Change Type
516 -1 porting notes
757 1 erw

Current commit bf055acb48
Reference commit 8a246bcb1c

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).

@joelriou joelriou added the WIP Work in progress label Mar 4, 2025
@mathlib4-dependent-issues-bot mathlib4-dependent-issues-bot added the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Mar 4, 2025
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mathlib4-dependent-issues-bot commented Mar 4, 2025

This PR/issue depends on:

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This PR has been migrated to a fork-based workflow: #30812

@joelriou joelriou closed this Oct 23, 2025
@YaelDillies YaelDillies deleted the jriou-left-resolution-reduced branch November 6, 2025 09:17
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