feat(Geometry/Manifold): MfldCat is a CartesianMonoidalCategory

[Deicyde]

We prove that the category of a C^n manifolds is a Cartesian monoidal category. This PR introduces a new file Geometry/Manifold/Category/MfldCat/CartesianMonoidal closely mirroring the structure of Algebra/Category/Grp/CartesianMonoidal.lean

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• depends on: feat(Geometry/Manifold): add MfldCat, the category of C^n manifolds #38223

[github-actions]

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[github-actions]

PR summary 9ee33d6428

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Geometry.Manifold.Category.MfldCat.Basic (new file)	2210
Mathlib.Geometry.Manifold.Category.MfldCat.CartesianMonoidal (new file)	2318

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Declarations diff

+ Hom
+ Hom.Simps.hom
+ Hom.hom
+ MfldCat
+ binaryProductLimitCone
+ cartesianMonoidalCategory
+ coe_comp
+ coe_id
+ coe_of
+ const
+ const_apply
+ diffeomorphOfIso
+ hom_comp
+ hom_id
+ hom_ofHom
+ id_apply
+ inhabited
+ instance : BraidedCategory (MfldCat.{u} 𝕜 n) := .ofCartesianMonoidalCategory
+ instance : Category (MfldCat 𝕜 n)
+ instance : CoeSort (MfldCat 𝕜 n) (Type u) := ⟨MfldCat.carrier⟩
+ instance : ConcreteCategory (MfldCat 𝕜 n)
+ instance : HasForget₂ (MfldCat 𝕜 n) TopCat.{u}
+ isTerminalPoint
+ isoOfDiffeomorph
+ ofHom
+ ofHom_comp
+ ofHom_hom
+ ofHom_id
+ ofNormedSpace
+ of_carrier
+ of_diffeomorphOfIso
+ of_isoOfDiffeomorph
+ point
+ prodObj
+ tensorObj_eq

You can run this locally as follows

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

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

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.

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Increase in tech debt: (relative, absolute) = (2.00, 0.01)

Current number	Change	Type
799	2	backward.privateInPublic
415	2	backward.privateInPublic.warn

Current commit 46643c4439
Reference commit 9ee33d6428

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:

• feat(Geometry/Manifold): add MfldCat, the category of C^n manifolds #38223
  By Dependent Issues (🤖). Happy coding!