Theorems · Definition · category theory

CategoryTheory.MonoOver.liftIso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {X : C} →
      {D : Type u₂} →
        [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
          {Y : D} →
            {F₁ F₂ : CategoryTheory.Functor (CategoryTheory.Over Y) (CategoryTheory.Over X)} →
              (h₁ :
                  ∀ (f : CategoryTheory.MonoOver Y),
                    CategoryTheory.Mono (F₁.obj ((CategoryTheory.MonoOver.forget Y).obj f)).hom) →
                (h₂ :
                    ∀ (f : CategoryTheory.MonoOver Y),
                      CategoryTheory.Mono (F₂.obj ((CategoryTheory.MonoOver.forget Y).obj f)).hom) →
                  (F₁ ≅ F₂) → (CategoryTheory.MonoOver.lift F₁ h₁ ≅ CategoryTheory.MonoOver.lift F₂ h₂)

Isomorphic functors Over Y ⥤ Over X lift to isomorphic functors MonoOver Y ⥤ MonoOver X.

Defined in

Mathlib.CategoryTheory.Subobject.MonoOver

Cited by

0 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category