Theorems · Theorem · category theory
CategoryTheory.Limits.hasLimit_of_hasColimit_leftOp
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {J : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} J]
(F : CategoryTheory.Functor J Cᵒᵖ) [CategoryTheory.Limits.HasColimit F.leftOp], CategoryTheory.Limits.HasLimit FIf F.leftOp : Jᵒᵖ ⥤ C has a colimit, we can construct a limit for F : J ⥤ Cᵒᵖ.
- Defined in
- Mathlib.CategoryTheory.Limits.Opposites
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.HasColimitstatement and proof · cited by 307
- CategoryTheory.Limits.HasLimitstatement · cited by 226
- CategoryTheory.Limits.colimit.isColimitproof · cited by 193
- CategoryTheory.Functor.leftOpstatement and proof · cited by 187
- CategoryTheory.Limits.colimit.coconeproof · cited by 136
- CategoryTheory.Limits.HasLimit.mkproof · cited by 29
- CategoryTheory.Limits.coneOfCoconeLeftOpproof · cited by 9
- CategoryTheory.Limits.isLimitConeOfCoconeLeftOpproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.hasLimitsOfShape_op_of_hasColimitsOfShapeproof · cited by 1
- CategoryTheory.Limits.hasColimit_leftOp_iff_hasLimitproof · cited by 1