Theorems · Theorem · category theory

CategoryTheory.Limits.preservesColimitsOfSize_of_op

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (F : CategoryTheory.Functor C D) [CategoryTheory.Limits.PreservesLimitsOfSize.{w, w', v₁, v₂, u₁, u₂} F.op],
  CategoryTheory.Limits.PreservesColimitsOfSize.{w, w', v₁, v₂, u₁, u₂} F

If F.op : Cᵒᵖ ⥤ Dᵒᵖ preserves limits, then F : C ⥤ D preserves colimits.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Opposites

Cited by

0 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesLimitsOfSize