feat(AlgebraicTopology/SimplicialSet): connected components of simplicial sets

[joelriou]

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• depends on: feat(AlgebraicTopology/SimplicialSet): evaluation on subcomplexes #37334

[github-actions]

PR summary a1ce43f036

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.AlgebraicTopology.SimplicialSet.SubcomplexEvaluation (new file)	886
Mathlib.AlgebraicTopology.SimplicialSet.Nonempty (new file)	908
Mathlib.AlgebraicTopology.SimplicialSet.PiZero (new file)	909

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Declarations diff

+ IsConnected
+ IsPreconnected
+ Nonempty
+ instance (T : Type u) [Preorder T] [Nonempty T] : (nerve T).Nonempty
+ instance (n : SimplexCategory) : (stdSimplex.obj n).Nonempty
+ instance (n : SimplexCategoryᵒᵖ) [X.Nonempty] : Nonempty (X.obj n)
+ instance [X.Nonempty] : Nonempty X.N := ⟨N.mk (n := 0) (Classical.arbitrary _) (by simp)⟩
+ instance [X.Nonempty] : Nonempty X.S := ⟨S.mk (dim := 0) (Classical.arbitrary _)⟩
+ instance {J : Type*} [Category* J] {X : SSet.{u}} [IsFilteredOrEmpty J] :
+ isInitialOfNotNonempty
+ lift
+ lift_mk
+ mapπ₀
+ mapπ₀_comp_apply
+ mapπ₀_id_apply
+ mapπ₀_mk
+ mk
+ mk_eq_mk_iff
+ mk_surjective
+ nonempty_of_hom
+ notNonempty_iff_hasDimensionLT_zero
+ ofSimplex_map_le
+ ofSimplex_map_of_epi
+ preimage_comp
+ preimage_ι
+ rec
+ sound
+ π₀
+ π₀Functor
+ π₀Rel
++ evaluation

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) = (1.00, 0.00)

Current number	Change	Type
6902	1	backward.isDefEq.respectTransparency

Current commit 347bf6dc18
Reference commit a1ce43f036

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).

[mathlib-dependent-issues]

This PR/issue depends on:

• feat(AlgebraicTopology/SimplicialSet): evaluation on subcomplexes #37334
  By Dependent Issues (🤖). Happy coding!