Theorems · Theorem · category theory
CategoryTheory.Limits.reflectsLimit_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] (K : CategoryTheory.Functor J Cᵒᵖ)
(F : CategoryTheory.Functor C Dᵒᵖ) [CategoryTheory.Limits.ReflectsColimit K.leftOp F],
CategoryTheory.Limits.ReflectsLimit K F.leftOpIf F : C ⥤ Dᵒᵖ reflects colimits of K.leftOp : Jᵒᵖ ⥤ C, then F.leftOp : Cᵒᵖ ⥤ D
reflects limits of K : J ⥤ Cᵒᵖ.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.Coneproof · cited by 710
- CategoryTheory.Limits.IsLimitproof · cited by 664
- CategoryTheory.Functor.leftOpstatement and proof · cited by 187
- CategoryTheory.Functor.mapConeproof · cited by 147
- CategoryTheory.Limits.ReflectsColimitstatement and proof · cited by 33
- CategoryTheory.Limits.ReflectsLimitstatement · cited by 31
- CategoryTheory.Limits.isColimitOfReflectsproof · cited by 19
- CategoryTheory.Limits.IsLimit.opproof · cited by 14
- CategoryTheory.Limits.isLimitOfCoconeLeftOpOfConeproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.reflectsLimitsOfShape_leftOpproof · cited by 4