Theorems · Theorem · category theory

CategoryTheory.LaxBraidedFunctor.comp_hom

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.BraidedCategory C] {D : Type u₂} [inst_3 : CategoryTheory.Category.{v₂, u₂} D]
  [inst_4 : CategoryTheory.MonoidalCategory D] [inst_5 : CategoryTheory.BraidedCategory D]
  {F G H : CategoryTheory.LaxBraidedFunctor C D} (α : F ⟶ G) (β : G ⟶ H),
  (CategoryTheory.CategoryStruct.comp α β).hom = CategoryTheory.CategoryStruct.comp α.hom β.hom

Defined in: Mathlib.CategoryTheory.Monoidal.Braided.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.MonoidalCategory CategoryTheory.BraidedCategory CategoryTheory.Category CategoryTheory.MonoidalCategory CategoryTheory.BraidedCategory

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Cites9

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.MonoidalCategorystatement and proof · cited by 3,095
CategoryTheory.InducedCategory.Hom.homstatement · cited by 850
CategoryTheory.BraidedCategorystatement and proof · cited by 779
CategoryTheory.LaxMonoidalFunctorstatement · cited by 96
CategoryTheory.LaxBraidedFunctorstatement and proof · cited by 33
CategoryTheory.LaxBraidedFunctor.toLaxMonoidalFunctorstatement · cited by 15

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.LaxBraidedFunctor.comp_hom_assocproof · cited by 0