feat(Geometry/Convex): the simplicial set of affine simplices of a convex space

[joelriou]

Let Y be a R-convex space. In this file, we introduce the simplicial set toSSet R Y whose n-simplices are affine maps from the standard n-dimensional simplex to Y. (When R := ℝ and Y has a suitable topology, this identifies to a subcomplex of the singular simplicial set of the topological space Y.)

From https://github.com/joelriou/excision

---

• depends on: feat(Geometry/Convex): the cone of an affine map from the standard simplex #43524

[github-actions]

PR summary 7c5278427f

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Geometry.Convex.ConvexSpace.AffineMapCone (new file)	1031
Mathlib.Geometry.Convex.ConvexSpace.ToSSet (new file)	1357

---

Declarations diff (regex)

+ AffineMap.cone
+ AffineMap.cone_comp
+ AffineMap.cone_def
+ AffineMap.cone_mk₁
+ AffineMap.cone_mk₂
+ AffineMap.cone_naturality
+ AffineMap.cone_single_succ
+ AffineMap.cone_single_zero
+ AffineMap.toSSetMap
+ toSSet
+ toSSet.cone
+ toSSet.cone_comp_d_eq_sub
+ toSSet.d_comp_cone_add_cone_comp_d
+ toSSet.d_comp_cone_eq_sub
+ toSSet.extraDegeneracy
+ toSSet.δ_affineMapMk
+ toSSet.δ_one_affineMapMk₂
+ toSSet.δ_one_affineMapMk₃
+ toSSet.δ_two_affineMapMk₃
+ toSSet.δ_zero
+ toSSet.δ_zero_affineMapMk₂
+ toSSet.δ_zero_affineMapMk₃
+ toSSet.ι_cone
+ toSSetAugmented
+ δ_apply
+ σ_apply

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 7c52784).

• +34 new declarations
• −0 removed declarations

+CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.mk.congr_simp
+Convexity.ConvexSpace.AffineMap.cone
+Convexity.ConvexSpace.AffineMap.cone_comp
+Convexity.ConvexSpace.AffineMap.cone_def
+Convexity.ConvexSpace.AffineMap.cone_mk₁
+Convexity.ConvexSpace.AffineMap.cone_mk₂
+Convexity.ConvexSpace.AffineMap.cone_naturality
+Convexity.ConvexSpace.AffineMap.cone_naturality_assoc
+Convexity.ConvexSpace.AffineMap.cone_single_succ
+Convexity.ConvexSpace.AffineMap.cone_single_zero
+Convexity.ConvexSpace.AffineMap.toSSetMap
+Convexity.ConvexSpace.AffineMap.toSSetMap_app
+Convexity.ConvexSpace.toSSet
+Convexity.ConvexSpace.toSSet.cone
+Convexity.ConvexSpace.toSSet.cone_comp_d_eq_sub
+Convexity.ConvexSpace.toSSet.d_comp_cone_add_cone_comp_d
+Convexity.ConvexSpace.toSSet.d_comp_cone_eq_sub
+Convexity.ConvexSpace.toSSet.extraDegeneracy
+Convexity.ConvexSpace.toSSet.extraDegeneracy_s
+Convexity.ConvexSpace.toSSet.extraDegeneracy_s'
+Convexity.ConvexSpace.toSSet.δ_affineMapMk
+Convexity.ConvexSpace.toSSet.δ_one_affineMapMk₂
+Convexity.ConvexSpace.toSSet.δ_one_affineMapMk₃
+Convexity.ConvexSpace.toSSet.δ_two_affineMapMk₃
+Convexity.ConvexSpace.toSSet.δ_zero
+Convexity.ConvexSpace.toSSet.δ_zero_affineMapMk₂
+Convexity.ConvexSpace.toSSet.δ_zero_affineMapMk₃
+Convexity.ConvexSpace.toSSet.ι_cone
+Convexity.ConvexSpace.toSSet.ι_cone_assoc
+Convexity.ConvexSpace.toSSetAugmented
+Convexity.ConvexSpace.toSSet_map
+Convexity.ConvexSpace.toSSet_obj
+SimplexCategory.δ_apply
+SimplexCategory.σ_apply

---

No changes to strong technical debt.

Increase in weak tech debt: (relative, absolute) = (2.00, 0.00)

Current number	Change	Type (weak)
exposed public sections	5051	2

Current commit 7c5278427f
Reference commit e3ea2ac394

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.py 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/Convex): the cone of an affine map from the standard simplex #43524
  By Dependent Issues (🤖). Happy coding!