[Merged by Bors] - feat(AlgebraicTopology): the monoidal category structure on simplicial sets #11396
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
leanprover-community-mathlib4-bot
added
the
blocked-by-other-PR
2 tasks
leanprover-community-mathlib4-bot
removed
the
blocked-by-other-PR
|
This PR/issue depends on:
|
joelriou
added
awaiting-review
adamtopaz
reviewed
Mar 19, 2024
Comment on lines
29
to
31
| instance : ChosenFiniteProducts SSet.{u} where | ||
| terminal := FunctorToTypes.functorEmptyLimitCone _ | ||
| product := FunctorToTypes.binaryProductLimitCone |
There was a problem hiding this comment.
It should now be possible to provide such an instance for the category of functors from C to D whenever D has chosen finite products. In fact, it seems that pretty much everything in this file can be similarly generalized.
There was a problem hiding this comment.
Thanks for the suggestions. The simp lemmas were slightly more difficult to obtain in general, but it works.
TwoFX
added
awaiting-author
joelriou
removed
the
awaiting-author
joelriou
added
awaiting-review
adamtopaz
approved these changes
Mar 29, 2024
There was a problem hiding this comment.
I'm perfectly happy with the code you wrote in the general context. In the case of the monoidal structure on simplicial sets, I had a slight concern that mixing the ChosenFiniteProducts api and the (type-theoretic) Prod, but it seems that the necessary simp lemmas already exist for the monoidal structure on Type*, so it seems that everything (especially simp) should work as expected!
Thanks!
bors r+
leanprover-community-mathlib4-bot
added
ready-to-merge
mathlib-bors bot
pushed a commit
that referenced
this pull request
Mar 29, 2024
…l sets (#11396) If a category `C` has chosen finite products, then the functor category `J ⥤ C` also. In particular, the category of simplicial sets is endowed with the monoidal category given by the explicit terminal object and binary products. Simplifications lemmas have also been added in the context of categories with chosen finite products. For terminal objects in such categories, the terminal object is given as a limit cone of `Functor.empty.{0} C` rather than `Functor.empty.{v} C` so as to be consistent with the limits API for terminal objects. Co-authored-by: Jack McKoen <mckoen@ualberta.ca>
|
Pull request successfully merged into master. Build succeeded: |
mathlib-bors
bot
changed the title
Louddy
pushed a commit
that referenced
this pull request
Apr 15, 2024
…l sets (#11396) If a category `C` has chosen finite products, then the functor category `J ⥤ C` also. In particular, the category of simplicial sets is endowed with the monoidal category given by the explicit terminal object and binary products. Simplifications lemmas have also been added in the context of categories with chosen finite products. For terminal objects in such categories, the terminal object is given as a limit cone of `Functor.empty.{0} C` rather than `Functor.empty.{v} C` so as to be consistent with the limits API for terminal objects. Co-authored-by: Jack McKoen <mckoen@ualberta.ca>
atarnoam
pushed a commit
that referenced
this pull request
Apr 16, 2024
…l sets (#11396) If a category `C` has chosen finite products, then the functor category `J ⥤ C` also. In particular, the category of simplicial sets is endowed with the monoidal category given by the explicit terminal object and binary products. Simplifications lemmas have also been added in the context of categories with chosen finite products. For terminal objects in such categories, the terminal object is given as a limit cone of `Functor.empty.{0} C` rather than `Functor.empty.{v} C` so as to be consistent with the limits API for terminal objects. Co-authored-by: Jack McKoen <mckoen@ualberta.ca>
uniwuni
pushed a commit
that referenced
this pull request
Apr 19, 2024
…l sets (#11396) If a category `C` has chosen finite products, then the functor category `J ⥤ C` also. In particular, the category of simplicial sets is endowed with the monoidal category given by the explicit terminal object and binary products. Simplifications lemmas have also been added in the context of categories with chosen finite products. For terminal objects in such categories, the terminal object is given as a limit cone of `Functor.empty.{0} C` rather than `Functor.empty.{v} C` so as to be consistent with the limits API for terminal objects. Co-authored-by: Jack McKoen <mckoen@ualberta.ca>
callesonne
pushed a commit
that referenced
this pull request
Apr 22, 2024
…l sets (#11396) If a category `C` has chosen finite products, then the functor category `J ⥤ C` also. In particular, the category of simplicial sets is endowed with the monoidal category given by the explicit terminal object and binary products. Simplifications lemmas have also been added in the context of categories with chosen finite products. For terminal objects in such categories, the terminal object is given as a limit cone of `Functor.empty.{0} C` rather than `Functor.empty.{v} C` so as to be consistent with the limits API for terminal objects. Co-authored-by: Jack McKoen <mckoen@ualberta.ca>
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.
If a category
Chas chosen finite products, then the functor categoryJ ⥤ Calso. In particular, the category of simplicial sets is endowed with the monoidal category given by the explicit terminal object and binary products.Simplifications lemmas have also been added in the context of categories with chosen finite products. For terminal objects in such categories, the terminal object is given as a limit cone of
Functor.empty.{0} Crather thanFunctor.empty.{v} Cso as to be consistent with the limits API for terminal objects.Co-authored-by: Jack McKoen mckoen@ualberta.ca