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Theorems · Theorem · category theory

CategoryTheory.Functor.Final.hasColimit_comp_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) [F.Final] {E : Type u₃} [inst_3 : CategoryTheory.Category.{v₃, u₃} E]
  {G : CategoryTheory.Functor D E}, CategoryTheory.Limits.HasColimit (F.comp G) ↔ CategoryTheory.Limits.HasColimit G
Defined in
Mathlib.CategoryTheory.Limits.Final
Cited by
1 results in Mathlib
Foundations
Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FinalCategoryTheory.Category
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Around this declaration

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CategoryTheory.TwoSquare.hasPointwiseLeftKanExtensionAt_iff · cited by 2TwoSquare.hasPointwiseLef…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Limits.HasColimit · cited by 307Limits.HasColimitCategoryTheory.Functor.Final · cited by 112Functor.FinalCategoryTheory.Functor.Final.hasColimit_of_comp · cited by 2Final.hasColimit_of_compFinal.hasColimit_comp_iffCITED BYCITES

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