Theorems · Theorem · category theory
CategoryTheory.SymmetricCategory.symmetry_assoc
∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {inst_1 : CategoryTheory.MonoidalCategory C}
[self : CategoryTheory.SymmetricCategory C] (X Y : C) {Z : C}
(h : CategoryTheory.MonoidalCategoryStruct.tensorObj X Y ⟶ Z),
CategoryTheory.CategoryStruct.comp (β_ X Y).hom (CategoryTheory.CategoryStruct.comp (β_ Y X).hom h) = h- Cited by
- 11 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Iso.homstatement and proof · cited by 7,684
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.MonoidalCategoryStruct.tensorObjstatement and proof · cited by 3,106
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.BraidedCategory.braidingstatement and proof · cited by 257
- CategoryTheory.SymmetricCategorystatement and proof · cited by 19
- CategoryTheory.SymmetricCategory.symmetryproof · cited by 5
Cited by11
Results whose statement or proof uses this declaration.
- CategoryTheory.Over.sectionsUncurry_sectionsCurryproof · cited by 2
- CategoryTheory.AddGrpObj.tensorHom_neg_neg_addproof · cited by 2
- CategoryTheory.GrpObj.tensorHom_inv_inv_mulproof · cited by 2
- CategoryTheory.Over.sectionsCurry_sectionUncurryproof · cited by 2
- CategoryTheory.AddGrpObj.add_neg_revproof · cited by 1
- CategoryTheory.bijection_symm_apply_idproof · cited by 1
- CategoryTheory.GradedObject.Monoidal.symmetryproof · cited by 1
- CategoryTheory.GrpObj.mul_inv_revproof · cited by 1
- CategoryTheory.MonoidalCategory.DayConvolution.symmetryproof · cited by 0
- CategoryTheory.Monoidal.Reflective.isIso_tfaeproof · cited by 0
- CategoryTheory.SymmetricCategory.rightDistrib_of_leftDistribproof · cited by 0