[Merged by Bors] - chore(CategoryTheory/Monoidal): oplax functors and comonoids #13312
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PR summary f9d9657ea4
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| File | Base Count | Head Count | Change |
|---|---|---|---|
| Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory | 465 | 468 | +3 (+0.65%) |
| Mathlib.CategoryTheory.Monoidal.Internal.Limits | 470 | 473 | +3 (+0.64%) |
Import changes for all files
| Files | Import difference |
|---|---|
Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory Mathlib.CategoryTheory.Monoidal.Internal.Limits |
3 |
Declarations diff
+ comonFunctorCategoryEquivalence
+ counitIso
+ forgetPreservesLimitsOfShape
+ functor
+ hasLimitsOfShape
++ functorObj
++ inverseObj
- Functor.obj
- Inverse.obj
- forgetPreservesLimits
- hasLimits
You can run this locally as follows
## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>
## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>
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🚀 Pull request has been placed on the maintainer queue by erdOne. |
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Thanks! bors merge |
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Oplax monoidal functors take comonoids to comonoids. Also, generalize constructions of limits in `Mon_` so limits of a particular shape in `C` are enough to give limits of that shape in `Mon_ C`. - [x] depends on: #13310 - [x] depends on: #13316 Co-authored-by: Scott Morrison <[email protected]> Co-authored-by: Joël Riou <[email protected]>
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Defines Hopf monoids in a braided category. Proves two facts (antipode is an antihomomorphism, morphisms intertwine antipode) that are not yet proved for unbundled Hopf algebras. Once we prove `Hopf_ (ModuleCat R)` is equivalent to `HopfAlgebraCat` (having defined that!), we will get those two facts for free. We should also check later that `Hopf_ C` in a cartesian monoidal category is equivalent `GroupObject_ C` (being defined independently elsewhere). - [x] depends on: #13313 - [x] depends on: #13312 (probably doesn't actually depend, but I don't want to sort out the git history now) - [x] depends on: #13315 Co-authored-by: Scott Morrison <[email protected]> Co-authored-by: Joël Riou <[email protected]>
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Defines Hopf monoids in a braided category. Proves two facts (antipode is an antihomomorphism, morphisms intertwine antipode) that are not yet proved for unbundled Hopf algebras. Once we prove `Hopf_ (ModuleCat R)` is equivalent to `HopfAlgebraCat` (having defined that!), we will get those two facts for free. We should also check later that `Hopf_ C` in a cartesian monoidal category is equivalent `GroupObject_ C` (being defined independently elsewhere). - [x] depends on: #13313 - [x] depends on: #13312 (probably doesn't actually depend, but I don't want to sort out the git history now) - [x] depends on: #13315 Co-authored-by: Scott Morrison <[email protected]> Co-authored-by: Joël Riou <[email protected]>
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Defines Hopf monoids in a braided category. Proves two facts (antipode is an antihomomorphism, morphisms intertwine antipode) that are not yet proved for unbundled Hopf algebras. Once we prove `Hopf_ (ModuleCat R)` is equivalent to `HopfAlgebraCat` (having defined that!), we will get those two facts for free. We should also check later that `Hopf_ C` in a cartesian monoidal category is equivalent `GroupObject_ C` (being defined independently elsewhere). - [x] depends on: #13313 - [x] depends on: #13312 (probably doesn't actually depend, but I don't want to sort out the git history now) - [x] depends on: #13315 Co-authored-by: Scott Morrison <[email protected]> Co-authored-by: Joël Riou <[email protected]>
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Defines Hopf monoids in a braided category. Proves two facts (antipode is an antihomomorphism, morphisms intertwine antipode) that are not yet proved for unbundled Hopf algebras. Once we prove `Hopf_ (ModuleCat R)` is equivalent to `HopfAlgebraCat` (having defined that!), we will get those two facts for free. We should also check later that `Hopf_ C` in a cartesian monoidal category is equivalent `GroupObject_ C` (being defined independently elsewhere). - [x] depends on: #13313 - [x] depends on: #13312 (probably doesn't actually depend, but I don't want to sort out the git history now) - [x] depends on: #13315 Co-authored-by: Scott Morrison <[email protected]> Co-authored-by: Joël Riou <[email protected]>
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Defines Hopf monoids in a braided category. Proves two facts (antipode is an antihomomorphism, morphisms intertwine antipode) that are not yet proved for unbundled Hopf algebras. Once we prove `Hopf_ (ModuleCat R)` is equivalent to `HopfAlgebraCat` (having defined that!), we will get those two facts for free. We should also check later that `Hopf_ C` in a cartesian monoidal category is equivalent `GroupObject_ C` (being defined independently elsewhere). - [x] depends on: #13313 - [x] depends on: #13312 (probably doesn't actually depend, but I don't want to sort out the git history now) - [x] depends on: #13315 Co-authored-by: Scott Morrison <[email protected]> Co-authored-by: Joël Riou <[email protected]>
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Oplax monoidal functors take comonoids to comonoids. Also, generalize constructions of limits in
Mon_so limits of a particular shape inCare enough to give limits of that shape inMon_ C.