Theorems · Theorem · category theory

CategoryTheory.Functor.fullyFaithfulCancelRight_hom_app

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {E : Type u₃} [inst_2 : CategoryTheory.Category.{v₃, u₃} E] {F G : CategoryTheory.Functor C D}
  {H : CategoryTheory.Functor D E} [inst_3 : H.Full] [inst_4 : H.Faithful] (comp_iso : F.comp H ≅ G.comp H) (X : C),
  (CategoryTheory.Functor.fullyFaithfulCancelRight H comp_iso).hom.app X = H.preimage (comp_iso.hom.app X)

Defined in

Mathlib.CategoryTheory.Functor.FullyFaithful

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FullCategoryTheory.Functor.Faithful