Theorems · Theorem · category theory
CategoryTheory.Limits.hasLimitsOfShape_opposite_opposite_iff
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {J : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} J],
CategoryTheory.Limits.HasLimitsOfShape Jᵒᵖ Cᵒᵖ ↔ CategoryTheory.Limits.HasColimitsOfShape J C- Defined in
- Mathlib.CategoryTheory.Limits.Opposites
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Limits.HasColimitsOfShapestatement and proof · cited by 308
- CategoryTheory.Limits.HasLimitsOfShapestatement and proof · cited by 223
- CategoryTheory.Equivalence.symmproof · cited by 195
- CategoryTheory.opOpEquivalenceproof · cited by 34
- CategoryTheory.Limits.hasColimitsOfShape_of_equivalenceproof · cited by 22
- CategoryTheory.Limits.hasColimitsOfShape_of_hasLimitsOfShape_opproof · cited by 6
- CategoryTheory.Limits.hasLimitsOfShape_op_of_hasColimitsOfShapeproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.hasWidePullbacks_opposite_iffproof · cited by 0
- CategoryTheory.Limits.hasFiniteWidePullbacks_opposite_iffproof · cited by 0