Theorems · Theorem · category theory
CategoryTheory.Limits.preservesColimitsOfShape_leftOp
∀ {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] (F : CategoryTheory.Functor C Dᵒᵖ)
[CategoryTheory.Limits.PreservesLimitsOfShape Jᵒᵖ F], CategoryTheory.Limits.PreservesColimitsOfShape J F.leftOpIf F : C ⥤ Dᵒᵖ preserves limits of shape Jᵒᵖ, then F.leftOp : Cᵒᵖ ⥤ D preserves colimits
of shape J.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Limits.PreservesColimitsOfShapestatement · cited by 222
- CategoryTheory.Functor.leftOpstatement · cited by 187
- CategoryTheory.Limits.PreservesLimitsOfShapestatement and proof · cited by 156
- CategoryTheory.Limits.preservesColimit_leftOpproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.preservesColimits_leftOpproof · cited by 0
- CategoryTheory.Limits.preservesFiniteColimits_leftOpproof · cited by 0
- CategoryTheory.Limits.preservesFiniteCoproducts_leftOpproof · cited by 0
- CategoryTheory.Limits.preservesColimitsOfSize_leftOpproof · cited by 0