feat(RepresentationTheory/Homological/ContCohomology): add inflation maps in continuous cohomology

[rmhi]

For a normal subgroup N of a topological group G, define the inflation maps
from H^n(G/N, \pi^N) to H^n(G, \pi), where H^n is the n-th continuous cohomology.
These maps are defined as a natural transformation.

• depends on: chore(RepresentationTheory/Homological/ContCohomology): refactor functoriality #41539

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[github-actions]

PR summary 9d3fd507c5

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
10 files Mathlib.Topology.Algebra.Group.ClosedSubgroup Mathlib.Topology.Algebra.Group.Extension Mathlib.Topology.Algebra.Group.Quotient Mathlib.Topology.Algebra.IsUniformGroup.Basic Mathlib.Topology.Algebra.Order.ArchimedeanDiscrete Mathlib.Topology.Algebra.ProperAction.AddTorsor Mathlib.Topology.Algebra.ProperAction.Basic Mathlib.Topology.Algebra.ProperAction.Torsor Mathlib.Topology.Covering.Quotient Mathlib.Topology.Maps.Strict.Basic	1
Mathlib.RepresentationTheory.Homological.ContCohomology.Inflation (new file)	1918

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Declarations diff (regex)

+ ResMap_eq
+ ResMap_id_left
+ ResMap_id_right
+ _root_.QuotientTopGroup.coe_mk
+ _root_.QuotientTopGroup.mk
+ _root_.TopRep.resolutionXRes
+ _root_.continuousCohomologyFunctor
+ cochainsResMap
+ cochainsResMap_comp
+ cochainsResMap_eq
+ cochainsResMap_f_eq
+ cochainsResMap_id
+ cochainsResMap_id_left
+ cochainsResMap_id_right
+ cocyclesResMap
+ cocyclesResMap_comp
+ cocyclesResMap_id
+ coind₁Res_id
+ comp_id
+ continuousCohomologyFunctor_obj
+ homogeneousCochainsFunctor
+ homogeneousCochainsFunctor_obj
+ homogeneousCochainsResNatTrans
+ homogeneousCochainsResNatTrans_app_f
+ homogeneousCochainsXRes
+ homogeneousCochainsXRes_succ
+ homogeneousCochainsXRes_zero
+ id_comp
+ inflApp
+ inflApp_naturality
+ inflApp_naturality_aux
+ inflNatTrans
+ inflι
+ inflιapp
+ inflιapp_apply
+ instance {H : Type*} [Monoid H] (φ : H →* G) : (resFunctor (k := k) φ).Additive
+ invariantsRes
+ invariantsResMap_eq
+ invariantsResMap_id
+ invariantsResNatTrans
+ le_relInvariantsRho_ker
+ ofHom_comp
+ relInvariants
+ relInvariantsFunctor
+ relInvariantsInfl
+ relInvariantsIntertwining
+ relInvariantsIntertwining'
+ relInvariantsRho
+ resMap
+ resMap_comp
+ resMap_id
+ resNatTrans
+ resNatTrans_app
+ resolution'Functor
+ resolution'Res
+ resolution'ResNatTrans
+ resolutionResMap
+ resolutionResMap_comp
+ resolutionResMap_comp_d
+ resolutionResMap_eq
+ resolutionResMap_id
+ resolutionResMap_id_fst
+ resolutionResMap_id_snd
+ resolutionResMap_succ
+ resolutionResMap_zero
+ resolutionXRes_comp
+ resolutionXRes_comp_d
+ resolutionXRes_id
+ resolutionXRes_naturality
+ resolutionXRes_succ
+ resolutionXRes_zero
+ rho_mem_relInvariants
+ π_resMap
- cochainsMap
- cochainsMap_comp
- cochainsMap_id
- cocyclesMap
- cocyclesMap_comp
- cocyclesMap_id
- map
- map_comp
- map_id
- π_map

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

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

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean -- pending)

Computed after the build finishes.

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit 9d3fd507c5
Reference commit 2d00c9242a

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/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).

[mathlib-dependent-issues]

This PR/issue depends on:

• chore(RepresentationTheory/Homological/ContCohomology): refactor functoriality #41539
  By Dependent Issues (🤖). Happy coding!