Theorems · Definition · category theory

CategoryTheory.CostructuredArrow.projectQuotient

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {S : CategoryTheory.Functor C D} →
          {T : D} →
            [CategoryTheory.Limits.HasFiniteColimits C] →
              [CategoryTheory.Limits.PreservesFiniteColimits S] →
                {A : CategoryTheory.CostructuredArrow S T} →
                  CategoryTheory.Subobject (Opposite.op A) → CategoryTheory.Subobject (Opposite.op A.left)

Every quotient of a costructured arrow can be projected to a quotient of the underlying object.

Defined in

Mathlib.CategoryTheory.Subobject.Comma

Cited by

4 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasFiniteColimitsCategoryTheory.Limits.PreservesFiniteColimits