Theorems · Theorem · category theory
CategoryTheory.MonoidalCategory.whiskerLeft_comp
∀ {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),
CategoryTheory.MonoidalCategoryStruct.whiskerLeft W (CategoryTheory.CategoryStruct.comp f g) =
CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft W f)
(CategoryTheory.MonoidalCategoryStruct.whiskerLeft W g)- Defined in
- Mathlib.CategoryTheory.Monoidal.Category
- Cited by
- 82 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.MonoidalCategoryStruct.whiskerLeftstatement · cited by 915
- CategoryTheory.MonoidalCategoryStruct.tensorHomproof · cited by 587
- CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHomproof · cited by 31
Cited by82
Results whose statement or proof uses this declaration.
- CategoryTheory.MonoidalCategory.whiskerLeft_comp_assocproof · cited by 18
- CategoryTheory.MonoidalCategory.leftUnitor_whiskerRightproof · cited by 9
- Bimod.AssociatorBimod.hom_left_act_hom'proof · cited by 5
- Bimod.AssociatorBimod.hom_right_act_hom'proof · cited by 5
- CategoryTheory.MonoidalCategory.associator_inv_naturalityproof · cited by 4
- CategoryTheory.Functor.Monoidal.whiskerLeft_μ_δproof · cited by 4
- CategoryTheory.MonoidalCategory.id_tensor_compproof · cited by 4
- CategoryTheory.MonoidalCategory.whiskerLeft_inv_homproof · cited by 4
- CategoryTheory.MonoidalCategory.tensor_left_unitalityproof · cited by 3
- CategoryTheory.MonoidalCategory.tensor_right_unitalityproof · cited by 3
- CategoryTheory.Mathlib.Tactic.MonTauto.add_assoc_negproof · cited by 3
- CategoryTheory.MonoidalCategory.leftUnitor_monoidalproof · cited by 3