[Merged by Bors] - feat(RingTheory/Coalgebra/Convolution): Algebra instance on convolution semiring

[hawkrobe]

This PR completes the algebraic structure on the convolution object.

---

I followed the pattern in Matrix/WithConv.lean which splits out IsScalarTower and SMulCommClass. Used in pre-Lie / Oudom–Guin constructions.

[github-actions]

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[github-actions]

PR summary 4acad02b6c

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ convAlgebra
+ convAlgebraMap_apply
+ instance [Monoid S] [DistribMulAction S A] [SMulCommClass R S A] [IsScalarTower S A A] :
+ instance [Monoid S] [DistribMulAction S A] [SMulCommClass R S A] [SMulCommClass S A A] :

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)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 4acad02).

• +4 new declarations
• −0 removed declarations

+LinearMap.convAlgebra
+LinearMap.convAlgebraMap_apply
+LinearMap.instIsScalarTowerWithConvId
+LinearMap.instSMulCommClassWithConvId

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 4acad02b6c
Reference commit 3db20e2c6e

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-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.

[themathqueen]

I don't think this hurts having. Thanks!

maintainer merge

[github-actions]

🚀 Pull request has been placed on the maintainer queue by themathqueen.

[riccardobrasca]

Thanks!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

• ci (staging) / Build
• ci (staging) / Lint style
• ci (staging) / Post-Build Step
• ci (staging) / Post-CI job