[Merged by Bors] - Feat: Add Yang-Baxter equation and the opposite braided monoidal category #10415
Conversation
This file contains 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
Shamrock-Frost
added
awaiting-review
joelriou
reviewed
Feb 11, 2024
![github-actions[bot]](https://avatars.githubusercontent.com/in/15368?s=60&v=4){kind=small}
Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
joelriou
reviewed
Feb 14, 2024
joelriou
reviewed
Feb 14, 2024
joelriou
reviewed
Feb 14, 2024
joelriou
reviewed
Feb 14, 2024
joelriou
added
awaiting-author
Shamrock-Frost
force-pushed
the
MonoidalOppositeStuff
branch
from
7ef83b3
to
aecb5ec
Compare
Shamrock-Frost
force-pushed
the
MonoidalOppositeStuff
branch
from
aecb5ec
to
1fa39b2
Compare
Shamrock-Frost
added
awaiting-review
yuma-mizuno
reviewed
Feb 15, 2024
| @@ -123,6 +128,30 @@ theorem braiding_naturality {X X' Y Y' : C} (f : X ⟶ Y) (g : X' ⟶ Y') : | |||
| rw [tensorHom_def' f g, tensorHom_def g f] | |||
| simp_rw [Category.assoc, braiding_naturality_left, braiding_naturality_right_assoc] | |||
|
|
|||
| theorem yang_baxter (X Y Z : C) : | |||
There was a problem hiding this comment.
Is there some reasons why you put associators at the both ends in the RHS? I think this is one possible choice, but we also have other choices.
There was a problem hiding this comment.
Sorry, I meant LHS, not RHS.
There was a problem hiding this comment.
I chose this way of writing it because it becomes an equality of maps X ⊗ Y ⊗ Z ⟶ Z ⊗ Y ⊗ X, both the domain and codomain being fully right associated. Also because it's what was easiest for the proof of associativity in mopBraidedFunctor. There are other choices we could make but I don't see a reason to prefer another
Shamrock-Frost
force-pushed
the
MonoidalOppositeStuff
branch
from
bb83ed6
to
b7015e4
Compare
yuma-mizuno
reviewed
Feb 15, 2024
1 task
joelriou
changed the title
joelriou
reviewed
Feb 16, 2024
joelriou
added
awaiting-author
Shamrock-Frost
added
awaiting-review
joelriou
reviewed
Feb 16, 2024
This comment was marked as off-topic.
This comment was marked as off-topic.
Sorry, something went wrong.
joelriou
reviewed
Feb 16, 2024
|
bors d+ |
|
✌️ Shamrock-Frost can now approve this pull request. To approve and merge a pull request, simply reply with |
github-actions
bot
added
delegated
and removed
awaiting-review
Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
|
bors merge |
mathlib-bors bot
pushed a commit
that referenced
this pull request
Feb 16, 2024
…gory (#10415) This PR adds some basics about monoidal opposite categories and their relation to the original category, as well as the Yang-Baxter equation for braided monoidal categories. It should be easy to define an action of the braid group on an object of a braided monoidal category from this.
|
Pull request successfully merged into master. Build succeeded: |
mathlib-bors
bot
changed the title
riccardobrasca
pushed a commit
that referenced
this pull request
Feb 18, 2024
…gory (#10415) This PR adds some basics about monoidal opposite categories and their relation to the original category, as well as the Yang-Baxter equation for braided monoidal categories. It should be easy to define an action of the braid group on an object of a braided monoidal category from this.
dagurtomas
pushed a commit
that referenced
this pull request
Mar 22, 2024
…gory (#10415) This PR adds some basics about monoidal opposite categories and their relation to the original category, as well as the Yang-Baxter equation for braided monoidal categories. It should be easy to define an action of the braid group on an object of a braided monoidal category from this.
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
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.
This PR adds some basics about monoidal opposite categories and their relation to the original category, as well as the Yang-Baxter equation for braided monoidal categories. It should be easy to define an action of the braid group on an object of a braided monoidal category from this.