Theorems · Theorem · category theory

CategoryTheory.Adjunction.preservesColimitsOfShape_iff

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C} (adj : F ⊣ G) {E : Type u₃}
  [inst_2 : CategoryTheory.Category.{v₃, u₃} E] (H : CategoryTheory.Functor D E) (J : Type u)
  [inst_3 : CategoryTheory.Category.{v, u} J] [CategoryTheory.Limits.HasColimitsOfShape J C] [G.Full] [G.Faithful],
  CategoryTheory.Limits.PreservesColimitsOfShape J H ↔ CategoryTheory.Limits.PreservesColimitsOfShape J (F.comp H)

Defined in

Mathlib.CategoryTheory.Adjunction.FullyFaithfulLimits

Cited by

1 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfShapeCategoryTheory.Functor.FullCategoryTheory.Functor.Faithful