File: Mathlib/CategoryTheory/Localization/DerivabilityStructure/Basic.lean

full_name: CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure
code: /-- A localizer morphism `Φ : LocalizerMorphism W₁ W₂` is a right derivability
structure if it has right resolutions and the 2-square where the left and right functors
are localizations functors for `W₁` and `W₂` are Guitart exact. -/
class IsRightDerivabilityStructure : Prop where
  hasRightResolutions : Φ.HasRightResolutions := by infer_instance
  guitartExact' : TwoSquare.GuitartExact ((Φ.catCommSq W₁.Q W₂.Q).iso).hom
goal: Prop

full_name: CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.guitartExact'
code: /-- A localizer morphism `Φ : LocalizerMorphism W₁ W₂` is a right derivability
structure if it has right resolutions and the 2-square where the left and right functors
are localizations functors for `W₁` and `W₂` are Guitart exact. -/
class IsRightDerivabilityStructure : Prop where
  hasRightResolutions : Φ.HasRightResolutions := by infer_instance
  guitartExact' : TwoSquare.GuitartExact ((Φ.catCommSq W₁.Q W₂.Q).iso).hom
goal: CategoryTheory.TwoSquare.GuitartExact
  (CategoryTheory.CatCommSq.iso Φ.functor W₁.Q W₂.Q (Φ.localizedFunctor W₁.Q W₂.Q)).hom

full_name: CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.hasRightResolutions
code: /-- A localizer morphism `Φ : LocalizerMorphism W₁ W₂` is a right derivability
structure if it has right resolutions and the 2-square where the left and right functors
are localizations functors for `W₁` and `W₂` are Guitart exact. -/
class IsRightDerivabilityStructure : Prop where
  hasRightResolutions : Φ.HasRightResolutions := by infer_instance
  guitartExact' : TwoSquare.GuitartExact ((Φ.catCommSq W₁.Q W₂.Q).iso).hom
goal: Φ.HasRightResolutions

full_name: CategoryTheory.LocalizerMorphism.isRightDerivabilityStructure_iff
code: lemma isRightDerivabilityStructure_iff [Φ.HasRightResolutions] (e : Φ.functor ⋙ L₂ ≅ L₁ ⋙ F) :
    Φ.IsRightDerivabilityStructure ↔ TwoSquare.GuitartExact e.hom 
goal: Φ.IsRightDerivabilityStructure ↔ CategoryTheory.TwoSquare.GuitartExact e.hom

full_name: CategoryTheory.LocalizerMorphism.guitartExact_of_isRightDerivabilityStructure'
code: lemma guitartExact_of_isRightDerivabilityStructure' [h : Φ.IsRightDerivabilityStructure]
    (e : Φ.functor ⋙ L₂ ≅ L₁ ⋙ F) : TwoSquare.GuitartExact e.hom 
goal: CategoryTheory.TwoSquare.GuitartExact e.hom

full_name: CategoryTheory.LocalizerMorphism.guitartExact_of_isRightDerivabilityStructure
code: lemma guitartExact_of_isRightDerivabilityStructure [Φ.IsRightDerivabilityStructure] :
    TwoSquare.GuitartExact ((Φ.catCommSq L₁ L₂).iso).hom 
goal: CategoryTheory.TwoSquare.GuitartExact (CategoryTheory.CatCommSq.iso Φ.functor L₁ L₂ (Φ.localizedFunctor L₁ L₂)).hom

full_name: CategoryTheory.LocalizerMorphism.instHasRightResolutionsIdOfContainsIdentities
code: instance [W₁.ContainsIdentities] : (LocalizerMorphism.id W₁).HasRightResolutions 
goal: (CategoryTheory.LocalizerMorphism.id W₁).HasRightResolutions

full_name: CategoryTheory.LocalizerMorphism.instIsRightDerivabilityStructureIdOfContainsIdentities
code: instance [W₁.ContainsIdentities] : (LocalizerMorphism.id W₁).IsRightDerivabilityStructure 
goal: (CategoryTheory.LocalizerMorphism.id W₁).IsRightDerivabilityStructure