Theorems · Theorem · category theory
CategoryTheory.MonoidalCategory.whiskerLeft_comp_assoc
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] (W : C)
{X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z) {Z_1 : C} (h : CategoryTheory.MonoidalCategoryStruct.tensorObj W Z ⟶ Z_1),
CategoryTheory.CategoryStruct.comp
(CategoryTheory.MonoidalCategoryStruct.whiskerLeft W (CategoryTheory.CategoryStruct.comp f g)) h =
CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft W f)
(CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft W g) h)- Defined in
- Mathlib.CategoryTheory.Monoidal.Category
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Category.assocproof · cited by 6,433
- CategoryTheory.MonoidalCategoryStruct.tensorObjstatement and proof · cited by 3,106
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.MonoidalCategoryStruct.whiskerLeftstatement and proof · cited by 915
- CategoryTheory.MonoidalCategory.whiskerLeft_compproof · cited by 82
Cited by18
Results whose statement or proof uses this declaration.
- CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitorproof · cited by 12
- CategoryTheory.eHom_whisker_cancelproof · cited by 2
- CategoryTheory.Enriched.FunctorCategory.enriched_assocproof · cited by 2
- CategoryTheory.Enriched.FunctorCategory.enriched_comp_idproof · cited by 2
- CategoryTheory.eHomWhiskerLeft_compproof · cited by 2
- HomologicalComplex.rightUnitor'_invproof · cited by 1
- CategoryTheory.MonoidalClosed.ihomCurry_ihomUncurryproof · cited by 1
- CategoryTheory.GradedObject.Monoidal.pentagon_invproof · cited by 1
- CategoryTheory.MonoidalCategory.tensorμ_comp_μ_tensorHom_μ_comp_μproof · cited by 1
- CategoryTheory.MonoidalCategory.DayConvolution.hexagon_forwardproof · cited by 0