Theorems · Theorem · category theory
CategoryTheory.IsCommMonObj.mul_comm_assoc
∀ {C : Type u₁} {inst : CategoryTheory.Category.{v₁, u₁} C} {inst_1 : CategoryTheory.MonoidalCategory C}
{inst_2 : CategoryTheory.BraidedCategory C} (X : C) {inst_3 : CategoryTheory.MonObj X}
[self : CategoryTheory.IsCommMonObj X] {Z : C} (h : X ⟶ Z),
CategoryTheory.CategoryStruct.comp (β_ X X).hom (CategoryTheory.CategoryStruct.comp CategoryTheory.MonObj.mul h) =
CategoryTheory.CategoryStruct.comp CategoryTheory.MonObj.mul h- Defined in
- Mathlib.CategoryTheory.Monoidal.Mon
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses Quot.sound
- Assumes
- CategoryTheory.IsCommMonObj
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Cites13
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 and proof · cited by 17,999
- CategoryTheory.Iso.homstatement and proof · cited by 7,684
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.BraidedCategorystatement and proof · cited by 779
- CategoryTheory.BraidedCategory.braidingstatement and proof · cited by 257
- CategoryTheory.MonObj.mulstatement and proof · cited by 230
- CategoryTheory.MonObjstatement and proof · cited by 199
- CategoryTheory.IsCommMonObjstatement and proof · cited by 37
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