Theorems · Theorem · category theory
CategoryTheory.Limits.hasLimitsOfShape_op_of_hasColimitsOfShape
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {J : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} J]
[CategoryTheory.Limits.HasColimitsOfShape Jᵒᵖ C], CategoryTheory.Limits.HasLimitsOfShape J CᵒᵖIf C has colimits of shape Jᵒᵖ, we can construct limits in Cᵒᵖ of shape J.
- Defined in
- Mathlib.CategoryTheory.Limits.Opposites
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites6
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.Functorproof · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Limits.HasColimitsOfShapestatement and proof · cited by 308
- CategoryTheory.Limits.HasLimitsOfShapestatement · cited by 223
- CategoryTheory.Limits.hasLimit_of_hasColimit_leftOpproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.hasLimitsOfShape_opposite_opposite_iffproof · cited by 2