Theorems · Theorem · category theory

CategoryTheory.Limits.preservesColimitsOfSize_of_rightOp

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

If F.rightOp : C ⥤ Dᵒᵖ preserves limits, then F : Cᵒᵖ ⥤ 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.Category CategoryTheory.Category CategoryTheory.Limits.PreservesLimitsOfSize

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functorstatement and proof · cited by 16,252
Oppositestatement and proof · cited by 8,081
CategoryTheory.Functor.rightOpstatement and proof · cited by 214
CategoryTheory.Limits.PreservesColimitsOfSizestatement · cited by 93
CategoryTheory.Limits.PreservesLimitsOfSizestatement and proof · cited by 51
CategoryTheory.Limits.preservesColimitsOfShape_of_rightOpproof · cited by 3

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