feat(RingTheory): bialgebra homs R[G] → R[H] are in bijection with group homs G → H

[YaelDillies]

... for abelian groups G and H. Furthermore, the convolution product on bialgebra homs corresponds to pointwise addition on group homs

Also generate more lemmas through to_additive and remove some unused set_options.

From Toric

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[github-actions]

PR summary aa7f1a59b5

Import changes exceeding 2%

%	File
+19.33%	Mathlib.RingTheory.Bialgebra.MonoidAlgebra

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.RingTheory.Bialgebra.MonoidAlgebra	1293	1543	+250 (+19.33%)

Import changes for all files

Files	Import difference
Mathlib.RingTheory.HopfAlgebra.MonoidAlgebra	244
Mathlib.RingTheory.Bialgebra.MonoidAlgebra	250

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Declarations diff (regex)

+ bialgEquivOfSubsingleton
+ bialgHom_ext
+ convMul_algHom_single_one
+ counit_domCongr
+ domCongrBialgHom
+ isGroupLikeElem_iff_mem_range_single_one
+ isGroupLikeElem_single_one
+ liftGroupLikeBialgHom
+ mapDomainBialgHomAddEquiv
+ mapDomainBialgHomEquiv
+ mapDomainBialgHomMulEquiv
+ mapDomainBialgHom_mapDomainOfBialgHom
+ mapDomainBialgHom_mul
+ mapDomainBialgHom_single
+ mapDomainOfBialgHom
+ mapDomainOfBialgHomFun
+ mapDomainOfBialgHom_comp
+ mapDomainOfBialgHom_id
+ mapDomainOfBialgHom_mapDomainBialgHom
+ single_mapDomainOfBialgHom
+ single_mapDomainOfBialgHomFun_one
+ span_isGroupLikeElem
++ bialgHom_ext'
++ comulAlgHom_comp_mapRingHom
++ convMul_bialgHom_single
++ counitAlgHom_comp_mapRingHom
++ isGroupLikeElem_iff_mem_range_of
++ isGroupLikeElem_of
++ liftMulEquiv
- _root_.AddMonoidAlgebra.mapDomainBialgHom

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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Decrease in strong tech debt: (relative, absolute) = (4.00, 0.00)

Current number	Change	Type (strong)
7129	-4	backward.isDefEq.respectTransparency

Decrease in weak tech debt: (relative, absolute) = (1.00, 0.00)

Current number	Change	Type (weak)
5017	-1	exposed public sections

Current commit aa7f1a59b5
Reference commit 46ff937713

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).