Theorems · Theorem · category theory

CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.epi_f

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : CategoryTheory.IsGrothendieckAbelian.{w, v, u} C] {X : C} {J : Type w}
  [inst_3 : CategoryTheory.SmallCategory J] {Y : CategoryTheory.Functor J C} {c : CategoryTheory.Limits.Cocone Y}
  (hc : CategoryTheory.Limits.IsColimit c) (z : X ⟶ c.pt) [CategoryTheory.IsFiltered J],
  CategoryTheory.Epi (CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.f z)

Defined in

Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ColimCoyoneda

Cited by

1 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.IsGrothendieckAbelianCategoryTheory.SmallCategoryCategoryTheory.IsFiltered