Theorems · Theorem · category theory

CategoryTheory.ChosenPullbacksAlong.Over.tensorObj_ext

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.ChosenPullbacks C] {X A : C}
  {Y Z : CategoryTheory.Over X} (f₁ f₂ : A ⟶ (CategoryTheory.MonoidalCategoryStruct.tensorObj Y Z).left),
  CategoryTheory.CategoryStruct.comp f₁ (CategoryTheory.ChosenPullbacksAlong.fst Y.hom Z.hom) =
      CategoryTheory.CategoryStruct.comp f₂ (CategoryTheory.ChosenPullbacksAlong.fst Y.hom Z.hom) →
    CategoryTheory.CategoryStruct.comp f₁ (CategoryTheory.ChosenPullbacksAlong.snd Y.hom Z.hom) =
        CategoryTheory.CategoryStruct.comp f₂ (CategoryTheory.ChosenPullbacksAlong.snd Y.hom Z.hom) →
      f₁ = f₂

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.Over

Cited by

1 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.ChosenPullbacks