Theorems · Theorem · category theory

CategoryTheory.CartesianMonoidalCategory.hom_ext

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {T X Y : C} (f g : T ⟶ CategoryTheory.MonoidalCategoryStruct.tensorObj X Y),
  CategoryTheory.CategoryStruct.comp f (CategoryTheory.SemiCartesianMonoidalCategory.fst X Y) =
      CategoryTheory.CategoryStruct.comp g (CategoryTheory.SemiCartesianMonoidalCategory.fst X Y) →
    CategoryTheory.CategoryStruct.comp f (CategoryTheory.SemiCartesianMonoidalCategory.snd X Y) =
        CategoryTheory.CategoryStruct.comp g (CategoryTheory.SemiCartesianMonoidalCategory.snd X Y) →
      f = g

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Basic

Cited by

46 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategory