Theorems · Theorem · category theory

CategoryTheory.Functor.essImage.liftFunctor_map

∀ {J : Type u_1} {C : Type u_2} {D : Type u_3} [inst : CategoryTheory.Category.{v_1, u_1} J]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} C] [inst_2 : CategoryTheory.Category.{v_3, u_3} D]
  (G : CategoryTheory.Functor J D) (F : CategoryTheory.Functor C D) [inst_3 : F.Full] [inst_4 : F.Faithful]
  (hG : ∀ (j : J), F.essImage (G.obj j)) {i j : J} (f : i ⟶ j),
  (CategoryTheory.Functor.essImage.liftFunctor G F hG).map f =
    F.preimage
      (CategoryTheory.CategoryStruct.comp (F.toEssImage.objObjPreimageIso { obj := G.obj i, property := ⋯ }).hom.hom
        (CategoryTheory.CategoryStruct.comp (G.map f)
          (F.toEssImage.objObjPreimageIso { obj := G.obj j, property := ⋯ }).inv.hom))

Defined in

Mathlib.CategoryTheory.EssentialImage

Cited by

0 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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