Theorems · Theorem · category theory

CategoryTheory.yonedaMon_naturality

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {M N X Y : C} [inst_2 : CategoryTheory.MonObj M] [inst_3 : CategoryTheory.MonObj N]
  (α : CategoryTheory.yonedaMonObj M ⟶ CategoryTheory.yonedaMonObj N) (f : X ⟶ Y) (g : Y ⟶ M),
  (CategoryTheory.ConcreteCategory.hom (α.app (Opposite.op X))) (CategoryTheory.CategoryStruct.comp f g) =
    CategoryTheory.CategoryStruct.comp f ((CategoryTheory.ConcreteCategory.hom (α.app (Opposite.op Y))) g)

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Mon

Cited by

1 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.MonObjCategoryTheory.MonObj