Theorems · Theorem · category theory

CategoryTheory.Limits.chosenCoend.hom_ext_iff

∀ {J : Type u_1} {C : Type u_2} [inst : CategoryTheory.Category.{v_1, u_2} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_1} J] {F : CategoryTheory.Functor Jᵒᵖ (CategoryTheory.Functor J C)}
  [inst_2 : CategoryTheory.Limits.ChosenCoendsOfShape J C] {X : C} {f g : CategoryTheory.Limits.chosenCoend F ⟶ X},
  f = g ↔
    ∀ (j : J),
      CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.chosenCoend.ι F j) f =
        CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.chosenCoend.ι F j) g

Defined in

Mathlib.CategoryTheory.Limits.Chosen.End

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.ChosenCoendsOfShape