Theorems · Definition · category theory
CategoryTheory.LocalizerMorphism.op
{C₁ : Type u₁} →
{C₂ : Type u₂} →
[inst : CategoryTheory.Category.{v₁, u₁} C₁] →
[inst_1 : CategoryTheory.Category.{v₂, u₂} C₂] →
{W₁ : CategoryTheory.MorphismProperty C₁} →
{W₂ : CategoryTheory.MorphismProperty C₂} →
CategoryTheory.LocalizerMorphism W₁ W₂ → CategoryTheory.LocalizerMorphism W₁.op W₂.opThe opposite localizer morphism LocalizerMorphism W₁.op W₂.op deduced
from Φ : LocalizerMorphism W₁ W₂.
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 64 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
- Oppositestatement · cited by 8,081
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Functor.opproof · cited by 997
- CategoryTheory.LocalizerMorphismstatement and proof · cited by 161
- CategoryTheory.LocalizerMorphism.functorproof · cited by 140
- CategoryTheory.MorphismProperty.opstatement · cited by 71
Cited by34
Results whose statement or proof uses this declaration.
- CategoryTheory.LocalizerMorphism.LeftResolution.opstatement · cited by 6
- CategoryTheory.LocalizerMorphism.RightResolution.unopstatement and proof · cited by 6
- CategoryTheory.LocalizerMorphism.LeftResolution.opEquivalencestatement · cited by 5
- CategoryTheory.LocalizerMorphism.LeftResolution.opFunctorstatement · cited by 4
- CategoryTheory.LocalizerMorphism.LeftResolution.unopstatement and proof · cited by 4
- CategoryTheory.LocalizerMorphism.RightResolution.opstatement · cited by 4
- CategoryTheory.LocalizerMorphism.RightResolution.unopFunctorstatement and proof · cited by 4
- CategoryTheory.LocalizerMorphism.isLeftDerivabilityStructure_iffproof · cited by 3
- CategoryTheory.LocalizerMorphism.isLeftDerivabilityStructure_iff_opstatement and proof · cited by 2
- CategoryTheory.LocalizerMorphism.hasLeftResolutions_iff_opstatement and proof · cited by 1
- CategoryTheory.LocalizerMorphism.hasRightResolutions_iff_opstatement and proof · cited by 1