feat(Algebra/Category/ModuleCat): the pseudofunctors which send a ring to its category of modules

[joelriou]

In this PR, we construct the pseudofunctor ModuleCat.restrictScalarsPseudofunctor : Pseudofunctor (LocallyDiscrete RingCatᵒᵖ) Cat which sends a ring R to its category of modules: the contravariant functoriality is given by the restriction of scalars functors. We also define ModuleCat.extendScalarsPseudofunctor : Pseudofunctor (LocallyDiscrete CommRingCat) Cat: the covariant functoriality is given by the extension of scalars functors.

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• [x] depends on: #18201

[github-actions[bot]]

PR summary 7e993308df

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
13 files Mathlib.Algebra.Category.ModuleCat.Differentials.Basic Mathlib.Algebra.Category.ModuleCat.ChangeOfRings Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf Mathlib.Algebra.Category.ModuleCat.EnoughInjectives Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits Mathlib.Algebra.Category.ModuleCat.Presheaf Mathlib.Algebra.Category.ModuleCat.Presheaf.EpiMono Mathlib.Algebra.Category.ModuleCat.Presheaf.Monoidal Mathlib.Algebra.Category.ModuleCat.Presheaf.Abelian Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward Mathlib.Algebra.Category.ModuleCat.Presheaf.ChangeOfRings Mathlib.Algebra.Category.ModuleCat.Presheaf.Free	1
Mathlib.Algebra.Category.ModuleCat.Pseudofunctor (new file)	1258

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Declarations diff

+ CommRingCat.moduleCatExtendScalarsPseudofunctor + CommRingCat.moduleCatRestrictScalarsPseudofunctor + RingCat.moduleCatRestrictScalarsPseudofunctor + extendRestrictScalarsAdj_homEquiv_apply + extendRestrictScalarsAdj_unit_app_apply + extendScalarsComp + extendScalarsComp_hom_app_one_tmul + extendScalarsId + extendScalarsId_hom_app_one_tmul + extendScalarsId_inv_app_apply + extendScalars_assoc + extendScalars_assoc' + extendScalars_comp_id + extendScalars_id_comp + homEquiv_extendScalarsComp + homEquiv_extendScalarsId + hom_ext

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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Increase in tech debt: (relative, absolute) = (5.00, 0.00)

Current number	Change	Type
1508	5	erw

Current commit 7e993308df Reference commit 42764fbc0a

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:

• ~~leanprover-community/mathlib4#18201~~ By Dependent Issues (🤖). Happy coding!

[joelriou]

This all looks good to me, the only problem is that there are a lot of erws. I looked into this (see zulip), and I think all but one of your erws (the comp_apply one) would not be necessary if there was a dsimp% elaborator. Then, instead of erw [lemma] you would type rw [dsimp% lemma]. Making such an elaborator should be very easy (if it does not already exist), and I might have time to do this on Sunday if you can wait for that. But I am happy to have this merged also. I also left some small comments that are more like questions and do not need fixing.

Is this related to the feature I suggested at https://leanprover.zulipchat.com/#narrow/channel/287929-mathlib4/topic/attribute.20simp_NF_my_lemma.3F/near/443101462

[mathlib-bors[bot]]

This PR was included in a batch that was canceled, it will be automatically retried

[mathlib-bors[bot]]

Build failed (retrying...):

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[fpvandoorn]

probably causing the bors failure After the batch is merged, please merge master

bors r- bors d+

[mathlib-bors[bot]]

:v: joelriou can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[mathlib-bors[bot]]

Canceled.

[joelriou]

Retrying...

bors merge

[mathlib-bors[bot]]

Pull request successfully merged into master.

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