Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.localEpi_mem_range_eq_inverseImage_epimorphisms

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {D : Type u_2}
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C}
  (adj : F ⊣ G) [G.Faithful] [G.Full],
  (CategoryTheory.ObjectProperty.localEpi fun x => x ∈ Set.range G.obj) =
    (CategoryTheory.MorphismProperty.epimorphisms D).inverseImage F

Defined in

Mathlib.CategoryTheory.MorphismProperty.LocalEpi

Cited by

1 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FaithfulCategoryTheory.Functor.Full