Theorems · Theorem · category theory

CategoryTheory.Limits.preservesFiniteLimits_of_leftOp

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (F : CategoryTheory.Functor C Dᵒᵖ) [CategoryTheory.Limits.PreservesFiniteColimits F.leftOp],
  CategoryTheory.Limits.PreservesFiniteLimits F

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

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Opposites

Cited by

0 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesFiniteColimits