refactor(CategoryTheory/Monoidal): add whiskering operators#6307
Draft
yuma-mizuno wants to merge 79 commits intomasterfrom
Draft
refactor(CategoryTheory/Monoidal): add whiskering operators#6307yuma-mizuno wants to merge 79 commits intomasterfrom
yuma-mizuno wants to merge 79 commits intomasterfrom
Conversation
kim-em
reviewed
Aug 5, 2023
Co-authored-by: Scott Morrison <scott@tqft.net>
kim-em
reviewed
Aug 6, 2023
kim-em
reviewed
Aug 6, 2023
kim-em
reviewed
Aug 6, 2023
kim-em
reviewed
Aug 6, 2023
kim-em
reviewed
Aug 6, 2023
Comment on lines
+548
to
+554
| calc | ||
| _ = 𝟙 _ ⊗≫ | ||
| X₁ ◁ ((β_ X₂ Y₁).hom ▷ (Y₂ ⊗ Z₁) ≫ (Y₁ ⊗ X₂) ◁ (β_ Y₂ Z₁).hom) ▷ Z₂ ⊗≫ | ||
| X₁ ◁ Y₁ ◁ (β_ X₂ Z₁).hom ▷ Y₂ ▷ Z₂ ⊗≫ 𝟙 _ := ?eq1 | ||
| _ = _ := ?eq2 | ||
| case eq1 => coherence | ||
| case eq2 => rw [← whisker_exchange]; coherence |
Contributor
There was a problem hiding this comment.
My preference is not to use this ?eqn style, but to write the proofs inline in the calc block, at least when the proofs are as short as these ones.
I'm happy to use this technique for multiline proofs needed in a calc block, however.
| Cones.postcompose_obj_π, NatTrans.comp_app, Functor.const_obj_obj, Monoidal.tensorObj_obj, | ||
| Monoidal.tensorUnit_obj, Monoidal.leftUnitor_hom_app] | ||
| conv_rhs => rw [← tensor_id_comp_id_tensor (limit.π X j)] | ||
| simp |
There was a problem hiding this comment.
[lint-style] reported by reviewdog 🐶
Suggested change
| simp | |
| simp? |
| Cones.postcompose_obj_π, NatTrans.comp_app, Functor.const_obj_obj, Monoidal.tensorObj_obj, | ||
| Monoidal.tensorUnit_obj, Monoidal.rightUnitor_hom_app] | ||
| conv_rhs => rw [← id_tensor_comp_tensor_id _ (limit.π X j)] | ||
| simp |
There was a problem hiding this comment.
[lint-style] reported by reviewdog 🐶
Suggested change
| simp | |
| simp? |
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
6 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
We introduce whiskering operators. This allows us to introduce a simp-normal form for morphisms in monoidal categories. Rewriting into simp-normal forms is especially useful when combined with the coherence tactic.
tensorLeftby using whiskering #10898𝟙 X ⊗ fwithX ◁ f#10912𝟙 X ⊗ fwithX ◁ f#11223