Theorems · Definition · category theory

CategoryTheory.StructuredArrow.projectSubobject

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {S : D} →
          {T : CategoryTheory.Functor C D} →
            [CategoryTheory.Limits.HasFiniteLimits C] →
              [CategoryTheory.Limits.PreservesFiniteLimits T] →
                {A : CategoryTheory.StructuredArrow S T} → CategoryTheory.Subobject A → CategoryTheory.Subobject A.right

Every subobject of a structured arrow can be projected to a subobject 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.HasFiniteLimitsCategoryTheory.Limits.PreservesFiniteLimits