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[Merged by Bors] - feat(CategoryTheory/Monoidal/Arrow): define monoidal structure on arrow category#33935

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[Merged by Bors] - feat(CategoryTheory/Monoidal/Arrow): define monoidal structure on arrow category#33935
mckoen wants to merge 46 commits intoleanprover-community:masterfrom
mckoen:arrow-monoidal

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@mckoen mckoen commented Jan 13, 2026

defines a monoidal category structure on the arrow category of a cartesian closed category.


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@mckoen mckoen added WIP Work in progress t-category-theory Category theory labels Jan 13, 2026
@github-actions github-actions bot added the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Jan 13, 2026
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github-actions bot commented Feb 2, 2026

PR summary 8ec19128ad

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.CategoryTheory.Monoidal.Limits.HasLimits (new file) 436
Mathlib.CategoryTheory.Monoidal.Closed.Braided (new file) 467
Mathlib.CategoryTheory.Monoidal.Limits.Shapes.Pullback (new file) 588
Mathlib.CategoryTheory.Monoidal.PushoutProduct (new file) 672
Mathlib.CategoryTheory.Monoidal.Arrow (new file) 675

Declarations diff

+ HasColimit.isoOfNatIso_ι_hom_whiskerRight
+ HasColimit.whiskerLeft_isoOfNatIso_ι_hom
+ Limits.inl_comp_pushoutSymmetry_hom_whiskerRight
+ Limits.inr_comp_pushoutSymmetry_hom_whiskerRight
+ Limits.pushout.associator_inv_naturality_right_condition
+ Limits.pushout.associator_naturality_left_condition
+ Limits.pushout.condition_whiskerRight
+ Limits.pushout.whiskerLeft_condition
+ Limits.whiskerLeft_inl_comp_pushoutSymmetry_hom
+ Limits.whiskerLeft_inr_comp_pushoutSymmetry_hom
+ associator
+ associator_naturality
+ braiding
+ colimit.whiskerLeft_ι_desc
+ colimit.ι_desc_whiskerRight
+ hexagon_forward
+ hexagon_reverse
+ inl_desc_whiskerRight
+ inl_isoPushout_hom_whiskerRight
+ inl_isoPushout_inv_whiskerRight
+ inr_desc_whiskerRight
+ inr_isoPushout_hom_whiskerRight
+ inr_isoPushout_inv_whiskerRight
+ instance [BraidedCategory C] (A : C) [Closed A] :
+ leftUnitor
+ leftUnitor_naturality
+ pentagon
+ pullbackHom
+ pushoutProduct
+ rightUnitor
+ rightUnitor_naturality
+ tensorHom_comp_tensorHom
+ triangle
+ w_whiskerRight
+ whiskerLeftIso
+ whiskerLeft_inl_desc
+ whiskerLeft_inl_isoPushout_hom
+ whiskerLeft_inl_isoPushout_inv
+ whiskerLeft_inr_desc
+ whiskerLeft_inr_isoPushout_hom
+ whiskerLeft_inr_isoPushout_inv
+ whiskerLeft_w
+ whiskerRightIso
++ in

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.


Increase in tech debt: (relative, absolute) = (14.00, 0.00)
Current number Change Type
6499 14 backward.isDefEq.respectTransparency

Current commit 81322185cc
Reference commit 8ec19128ad

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 mathlib-dependent-issues bot added blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) and removed blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) labels Feb 5, 2026
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Comment thread Mathlib/CategoryTheory/Monoidal/Arrow.lean Outdated
@mckoen mckoen removed the awaiting-author A reviewer has asked the author a question or requested changes. label Mar 26, 2026
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mckoen commented Apr 1, 2026

I made a new file specifically for pushout-product stuff, which I think is better for future PRs.

@mckoen mckoen added the awaiting-CI This PR does not pass CI yet. This label is automatically removed once it does. label Apr 1, 2026
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@github-actions github-actions bot removed the large-import Automatically added label for PRs with a significant increase in transitive imports label Apr 13, 2026
@mckoen mckoen added the awaiting-CI This PR does not pass CI yet. This label is automatically removed once it does. label Apr 13, 2026
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Comment thread Mathlib/CategoryTheory/Monoidal/Limits/Shapes/Pullback.lean Outdated
Comment thread Mathlib/CategoryTheory/Monoidal/Limits/Shapes/Pullback.lean Outdated
@joelriou joelriou added the awaiting-author A reviewer has asked the author a question or requested changes. label Apr 13, 2026
@mckoen mckoen removed the awaiting-author A reviewer has asked the author a question or requested changes. label Apr 13, 2026
Comment thread Mathlib/CategoryTheory/Monoidal/PushoutProduct.lean Outdated
@joelriou joelriou added the awaiting-author A reviewer has asked the author a question or requested changes. label Apr 13, 2026
@mckoen mckoen removed the awaiting-author A reviewer has asked the author a question or requested changes. label Apr 13, 2026
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Thanks!

bors merge

mathlib-bors bot pushed a commit that referenced this pull request Apr 15, 2026
…ow category (#33935)

defines a monoidal category structure on the arrow category of a cartesian closed category.
@mathlib-triage mathlib-triage bot added ready-to-merge This PR has been sent to bors. and removed maintainer-merge A reviewer has approved the changed; awaiting maintainer approval. labels Apr 15, 2026
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mathlib-bors bot commented Apr 15, 2026

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat(CategoryTheory/Monoidal/Arrow): define monoidal structure on arrow category [Merged by Bors] - feat(CategoryTheory/Monoidal/Arrow): define monoidal structure on arrow category Apr 15, 2026
@mathlib-bors mathlib-bors bot closed this Apr 15, 2026
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