Theorems · Theorem · category theory

CategoryTheory.Limits.Concrete.isColimit_exists_of_rep_eq

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {FC : C → C → Type u_1} {CC : C → Type s}
  [inst_1 : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)] [inst_2 : CategoryTheory.ConcreteCategory C FC] {J : Type w}
  [inst_3 : CategoryTheory.Category.{r, w} J] (F : CategoryTheory.Functor J C)
  [CategoryTheory.Limits.PreservesColimit F (CategoryTheory.forget C)] [CategoryTheory.IsFiltered J]
  {D : CategoryTheory.Limits.Cocone F} {i j : J} (hD : CategoryTheory.Limits.IsColimit D)
  (x : CategoryTheory.ToType (F.obj i)) (y : CategoryTheory.ToType (F.obj j)),
  (CategoryTheory.ConcreteCategory.hom (D.ι.app i)) x = (CategoryTheory.ConcreteCategory.hom (D.ι.app j)) y →
    ∃ k f g, (CategoryTheory.ConcreteCategory.hom (F.map f)) x = (CategoryTheory.ConcreteCategory.hom (F.map g)) y

Defined in

Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic

Cited by

2 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesColimitCategoryTheory.IsFiltered