feat(CategoryTheory): add MorphismProperty.paths

[peabrainiac]

For any W : MorphismProperty C, we define W.paths : MorphismProperty (Paths C) as the morphism property containing those paths that consist entirely of morphisms in W.

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I'm currently preparing a PR defining replete subcategories and showing that the replete subcategories of any fixed category form a complete lattice; this API was written because it is helpful to characterise the subcategory generated by a class of morphisms W as (up to some issues regarding identities) consisting of those morphisms f which are the concatenation of a finitely many morphisms in W, i.e. for which there exists a path p with composePath p = f and W.paths p.

[github-actions]

PR summary f99e871a37

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.CategoryTheory.PathCategory.Basic	406	407	+1 (+0.25%)

Import changes for all files

Files	Import difference
5 files Mathlib.CategoryTheory.Bicategory.Coherence Mathlib.CategoryTheory.Groupoid.FreeGroupoid Mathlib.CategoryTheory.Groupoid.Subgroupoid Mathlib.CategoryTheory.Groupoid.VertexGroup Mathlib.CategoryTheory.PathCategory.Basic	1

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Declarations diff

+ comp_mem_paths_iff
+ composePath_mem
+ composePath_mem'
+ cons_mem_paths
+ cons_mem_paths_iff
+ instance (W : MorphismProperty C) : W.paths.IsMultiplicative
+ monotone_paths
+ nil_mem_paths
+ paths
+ paths_le_inverseImage
+ toPath_mem_paths
+ toPath_mem_paths_iff

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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No changes to technical debt.

You can run this locally as

./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).

[joelriou]

Are there lemmas that could make the connection with https://leanprover-community.github.io/mathlib4_docs/Mathlib/CategoryTheory/MorphismProperty/Composition.html#CategoryTheory.MorphismProperty.multiplicativeClosure