Theorems · Theorem · category theory

CategoryTheory.CartesianMonoidalCategory.whiskerRight_snd_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C] {X Y : C}
  (f : X ⟶ Y) (Z : C) {Z_1 : C} (h : Z ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight f Z)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.SemiCartesianMonoidalCategory.snd Y Z) h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.SemiCartesianMonoidalCategory.snd X Z) h

Defined in: Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.CartesianMonoidalCategory

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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 and proof · cited by 17,999
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
CategoryTheory.MonoidalCategoryStruct.whiskerRightstatement and proof · cited by 903
CategoryTheory.SemiCartesianMonoidalCategory.sndstatement and proof · cited by 181
CategoryTheory.CartesianMonoidalCategory.whiskerRight_sndproof · cited by 16

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.CartesianMonoidalCategory.tensorHom_sndproof · cited by 12
CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.associator_naturalityproof · cited by 0