Theorems · Definition · category theory

CategoryTheory.MonoOver.lift

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

Lift a functor between over categories to a functor between MonoOver categories, given suitable evidence that morphisms are taken to monomorphisms.

Defined in

Mathlib.CategoryTheory.Subobject.MonoOver

Cited by

8 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category