Theorems · Theorem · category theory

CategoryTheory.Limits.preservesLimit_of_op

∀ {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 C D) [CategoryTheory.Limits.PreservesColimit K.op F.op],
  CategoryTheory.Limits.PreservesLimit K F

If F.op : Cᵒᵖ ⥤ Dᵒᵖ preserves colimits of K.op : Jᵒᵖ ⥤ Cᵒᵖ, then F : C ⥤ D preserves limits 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.PreservesColimit