Theorems · Theorem · category theory

CategoryTheory.CostructuredArrow.projectQuotient_factors

∀ {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} [inst_2 : CategoryTheory.Limits.HasFiniteColimits C]
  [inst_3 : CategoryTheory.Limits.PreservesFiniteColimits S] {A : CategoryTheory.CostructuredArrow S T}
  (P : CategoryTheory.Subobject (Opposite.op A)),
  ∃ q,
    CategoryTheory.CategoryStruct.comp (S.map (CategoryTheory.CostructuredArrow.projectQuotient P).arrow.unop) q = A.hom

Defined in

Mathlib.CategoryTheory.Subobject.Comma

Cited by

0 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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