Theorems · Theorem · category theory
CategoryTheory.GradedObject.Monoidal.symmetry
∀ {I : Type u_1} [inst : AddCommMonoid I] {C : Type u_2} [inst_1 : CategoryTheory.Category.{v_1, u_2} C]
[inst_2 : CategoryTheory.MonoidalCategory C] (X Y : CategoryTheory.GradedObject I C)
[inst_3 : CategoryTheory.SymmetricCategory C] [inst_4 : X.HasTensor Y] [inst_5 : Y.HasTensor X],
CategoryTheory.CategoryStruct.comp (CategoryTheory.GradedObject.Monoidal.braiding X Y).hom
(CategoryTheory.GradedObject.Monoidal.braiding Y X).hom =
CategoryTheory.CategoryStruct.id (CategoryTheory.GradedObject.Monoidal.tensorObj X Y)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- AddCommMonoidstatement and proof · cited by 12,281
- CategoryTheory.Iso.homstatement and proof · cited by 7,684
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.BraidedCategory.braidingproof · cited by 257
- CategoryTheory.GradedObjectstatement and proof · cited by 239
- CategoryTheory.GradedObject.Monoidal.tensorObjstatement and proof · cited by 54
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.GradedObject.Monoidal.symmetry_assocproof · cited by 0