feat(CategoryTheory): composition of profunctors

[dagurtomas]

---

• depends on: [Merged by Bors] - feat(CategoryTheory): define profunctors #38085
• depends on: [Merged by Bors] - feat(CategoryTheory/Limits): explicit coends in Type #38382

[github-actions]

PR summary 42cfb88564

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.CategoryTheory.Profunctor.Comp (new file)	468

---

Declarations diff (regex)

+ associator
+ associatorComponents
+ comp
+ compDiagram
+ compDiagramMap
+ compDiagramMap_comp
+ compDiagramMap_id
+ comp_whiskerLeft
+ comp_whiskerRight
+ id_whiskerLeft
+ id_whiskerRight
+ leftUnitor
+ rightUnitor
+ univComp
+ whiskerLeft
+ whiskerLeft_comp
+ whiskerLeft_id
+ whiskerRight
+ whiskerRight_comp
+ whiskerRight_id
+ whisker_assoc
+ whisker_exchange

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 42cfb88).

• +42 new declarations
• −0 removed declarations

+CategoryTheory.Profunctor.associator
+CategoryTheory.Profunctor.associatorComponents
+CategoryTheory.Profunctor.associatorComponents_hom
+CategoryTheory.Profunctor.associatorComponents_inv
+CategoryTheory.Profunctor.associator_hom_app_app
+CategoryTheory.Profunctor.associator_inv_app_app
+CategoryTheory.Profunctor.comp
+CategoryTheory.Profunctor.compDiagram
+CategoryTheory.Profunctor.compDiagramMap
+CategoryTheory.Profunctor.compDiagramMap_app_app
+CategoryTheory.Profunctor.compDiagramMap_comp
+CategoryTheory.Profunctor.compDiagramMap_id
+CategoryTheory.Profunctor.compDiagram_map_app
+CategoryTheory.Profunctor.compDiagram_obj_map
+CategoryTheory.Profunctor.compDiagram_obj_obj
+CategoryTheory.Profunctor.comp_map_app
+CategoryTheory.Profunctor.comp_obj_map
+CategoryTheory.Profunctor.comp_obj_obj
+CategoryTheory.Profunctor.comp_whiskerLeft
+CategoryTheory.Profunctor.comp_whiskerRight
+CategoryTheory.Profunctor.id_whiskerLeft
+CategoryTheory.Profunctor.id_whiskerRight
+CategoryTheory.Profunctor.leftUnitor
+CategoryTheory.Profunctor.leftUnitor_hom_app_app
+CategoryTheory.Profunctor.leftUnitor_inv_app_app
+CategoryTheory.Profunctor.rightUnitor
+CategoryTheory.Profunctor.rightUnitor_hom_app_app
+CategoryTheory.Profunctor.rightUnitor_inv_app_app
+CategoryTheory.Profunctor.univComp
+CategoryTheory.Profunctor.univComp_map_app
+CategoryTheory.Profunctor.univComp_obj_map
+CategoryTheory.Profunctor.univComp_obj_obj
+CategoryTheory.Profunctor.whiskerLeft
+CategoryTheory.Profunctor.whiskerLeft_app_app
+CategoryTheory.Profunctor.whiskerLeft_comp
+CategoryTheory.Profunctor.whiskerLeft_id
+CategoryTheory.Profunctor.whiskerRight
+CategoryTheory.Profunctor.whiskerRight_app_app
+CategoryTheory.Profunctor.whiskerRight_comp
+CategoryTheory.Profunctor.whiskerRight_id
+CategoryTheory.Profunctor.whisker_assoc
+CategoryTheory.Profunctor.whisker_exchange

---

Increase in strong tech debt: (relative, absolute) = (8.56, 0.00)

Current number	Change	Type (strong)
4538	9	backward.defeqAttrib.useBackward
5690	8	backward.isDefEq.respectTransparency

Increase in weak tech debt: (relative, absolute) = (1.00, 0.00)

Current number	Change	Type (weak)
4997	1	exposed public sections

Current commit 42cfb88564
Reference commit 50b02783d6

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).

[robin-carlier]

Is there a way to spin things so that this one (and the one below) is private?
(I can get that to work by replacing the exact associatorComponents_aux₁ _ _ _ h₁ with exact (by exact associatorComponents_aux₁ _ _ _ h₁) in the def of associator component, but this is quite ugly.

[dagurtomas]

exact by exact feels like a hack (why doesn't it just do the same thing as exact?). But I agree these should ideally be private. I don't know a good solution

[dagurtomas]

Moved the bicategory to a followup PR: #39619

[adamtopaz]

Please make sure to update the "future work" section in the docs of Profunctor/Basic.lean.