Theorems · Definition · category theory

CategoryTheory.Subobject.lower

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {X : C} →
      {D : Type u₂} →
        [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
          {Y : D} →
            CategoryTheory.Functor (CategoryTheory.MonoOver X) (CategoryTheory.MonoOver Y) →
              CategoryTheory.Functor (CategoryTheory.Subobject X) (CategoryTheory.Subobject Y)

Any functor MonoOver X ⥤ MonoOver Y descends to a functor Subobject X ⥤ Subobject Y, because MonoOver Y is thin.

Defined in

Mathlib.CategoryTheory.Subobject.Basic

Cited by

6 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category