[Merged by Bors] - feat(Algebra/ModuleCat): exactness of restrictScalars for general universe level

[Thmoas-Guan]

Currently exactness of ModuleCat.restrictScalars is synth via being adjoint functor, however this needs the universe level to be some max u v where u is the universe level of the ring. Here we provide exactness of restrictScalars for general universe level using it preserves short exact sequence.

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[github-actions]

PR summary f394bad6a0

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Algebra.Category.ModuleCat.ChangeOfRingsExact (new file)	1368

---

Declarations diff (regex)

+ ModuleCat.restrictScalars_map_exact
+ instance : Limits.PreservesFiniteColimits (ModuleCat.restrictScalars.{v} f) := by
+ instance : Limits.PreservesFiniteLimits (ModuleCat.restrictScalars.{v} f) := by

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 f394bad).

• +3 new declarations
• −0 removed declarations

+ModuleCat.restrictScalars_map_exact
+instPreservesFiniteColimitsModuleCatRestrictScalars
+instPreservesFiniteLimitsModuleCatRestrictScalars

---

No changes to strong technical debt.

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

Current number	Change	Type (weak)
4926	1	exposed public sections

Current commit f394bad6a0
Reference commit 97f12126be

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).

[riccardobrasca]

Can you improve the docstring of the file giving the same explanation as in the PR description? Thanks!

bors d+

[mathlib-bors]

✌️ Thmoas-Guan can now approve this pull request until 2026-06-24 15:35 UTC (in 2 weeks). To approve and merge, reply with bors r+. More detailed instructions are available here.

⚠️ This delegation only covers changes within Archive/**, Counterexamples/**, docs/**, DownstreamTest/**, Mathlib/**, MathlibTest/**, widget/**, Archive.lean, Counterexamples.lean, docs.lean, Mathlib.lean; an author commit touching anything else will revoke it. Bors also revokes it if a later push changes too many files for it to check the full list — even if it stays within scope.

[Thmoas-Guan]

bors r+

[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