Theorems · Theorem · category theory

CategoryTheory.CartesianMonoidalCategory.whiskerLeft_fst_assoc

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

Defined in: Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
Cited by: 1 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.whiskerLeftstatement and proof · cited by 915
CategoryTheory.SemiCartesianMonoidalCategory.fststatement and proof · cited by 184
CategoryTheory.CartesianMonoidalCategory.whiskerLeft_fstproof · cited by 24

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.associator_naturalityproof · cited by 0