Theorems · Theorem · category theory

CategoryTheory.Limits.chosenCoend.hom_ext

∀ {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},
  (∀ (j : J),
      CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.chosenCoend.ι F j) f =
        CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.chosenCoend.ι F j) g) →
    f = g

Morphisms out of the chosen coend are determined by their composites with chosenCoend.ι.

Defined in

Mathlib.CategoryTheory.Limits.Chosen.End

Cited by

3 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.ChosenCoendsOfShape