Theorems · Theorem · category theory

CategoryTheory.Limits.reflectsColimit_unop

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {J : Type w} [inst_2 : CategoryTheory.Category.{w', w} J] (K : CategoryTheory.Functor J C)
  (F : CategoryTheory.Functor Cᵒᵖ Dᵒᵖ) [CategoryTheory.Limits.ReflectsLimit K.op F],
  CategoryTheory.Limits.ReflectsColimit K F.unop

If F : Cᵒᵖ ⥤ Dᵒᵖ reflects limits of K.op : Jᵒᵖ ⥤ Cᵒᵖ, then F.unop : C ⥤ D reflects colimits of K : J ⥤ C.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Opposites

Cited by

1 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.ReflectsLimit