feat: Tannaka duality for finite groups

[ybenmeur]

Proves Tannaka duality for finite groups.

• depends on: feat: some lemmas for Tannaka duality for finite groups #22174

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[github-actions]

PR summary 677b3fd017

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.RepresentationTheory.Tannaka (new file)	1735

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Declarations diff

+ algHomOfRightFDRepComp
+ auxFDRepHom
+ auxLinearMap
+ auxLinearMap_single_id
+ equiv
+ equivApp
+ equivHom
+ equivHom_inj
+ equivHom_surj
+ eval_of_alghom
+ forget
+ instance (V : FDRep R G) : AddCommGroup V := by
+ instance (V : FDRep R G) : Module R V := by
+ instance (V : FDRep R G) : Module.Finite R V := by
+ instance : (forget₂ (FDRep k G) (FGModuleCat k)).Monoidal := by
+ instance : CoeSort (FDRep R G) (Type u)
+ instance : ConcreteCategory (FDRep R G) (Action.HomSubtype _ _) := inferInstance
+ instance : HasForget₂ (FDRep R G) (Rep R G)
+ instance : LargeCategory (FDRep R G) := inferInstance
+ instance : Linear R (FDRep R G) := by infer_instance
+ instance : Preadditive (FDRep R G) := inferInstance
+ leftRegular
+ leftRegularFDRepHom
+ map_mul_toRightFDRepComp
+ mulRepHom
+ rightFDRep
+ rightRegular
+ tannaka_duality
+ toRightFDRepComp
+ toRightFDRepComp_in_rightRegular
+ toRightFDRepComp_inj
- instance (V : FDRep k G) : AddCommGroup V := by
- instance (V : FDRep k G) : Module k V := by
- instance : CoeSort (FDRep k G) (Type u)
- instance : ConcreteCategory (FDRep k G) (Action.HomSubtype _ _) := inferInstance
- instance : HasForget₂ (FDRep k G) (Rep k G)
- instance : LargeCategory (FDRep k G) := inferInstance
- instance : Linear k (FDRep k G) := by infer_instance
- instance : Preadditive (FDRep k G) := inferInstance

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).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• feat: some lemmas for Tannaka duality for finite groups #22174
  By Dependent Issues (🤖). Happy coding!

[jcommelin]

Hi! It's really cool to see this formalized. Note that your entire proof works verbatim over domains, and mostly even over (nontrivial) commutative rings.
I've just created #22235 for the generalization of FDRep.

See 80f3a63 for the generalization.