File: Mathlib/Algebra/Category/ModuleCat/Sheaf/Limits.lean

full_name: PresheafOfModules.isSheaf_of_isLimit
code: lemma isSheaf_of_isLimit : Presheaf.IsSheaf J (c.pt.presheaf) 
goal: CategoryTheory.Presheaf.IsSheaf J c.pt.presheaf

full_name: SheafOfModules.instSmallElemForallObjCompModuleCatαRingOppositeRingCatValPresheafOfModulesForgetEvaluationForgetSections
code: instance (X : Cᵒᵖ) : Small.{v} (((F ⋙ forget _) ⋙ PresheafOfModules.evaluation _ X) ⋙
    CategoryTheory.forget _).sections 
goal: Small.{v, max u₂ v}
  ↑(((F ⋙ SheafOfModules.forget R) ⋙ PresheafOfModules.evaluation R.val X) ⋙
        CategoryTheory.forget (ModuleCat ↑(R.val.obj X))).sections

full_name: SheafOfModules.createsLimit
code: noncomputable instance createsLimit : CreatesLimit F (forget _) 
goal: CategoryTheory.CreatesLimit F (SheafOfModules.forget R)

full_name: SheafOfModules.hasLimit
code: instance hasLimit : HasLimit F 
goal: CategoryTheory.Limits.HasLimit F

full_name: SheafOfModules.evaluationPreservesLimit
code: noncomputable instance evaluationPreservesLimit (X : Cᵒᵖ) :
    PreservesLimit F (evaluation R X) 
goal: CategoryTheory.Limits.PreservesLimit F (SheafOfModules.evaluation R X)

full_name: SheafOfModules.hasLimitsOfShape
code: instance hasLimitsOfShape : HasLimitsOfShape D (SheafOfModules.{v} R) 
goal: CategoryTheory.Limits.HasLimitsOfShape D (SheafOfModules R)

full_name: SheafOfModules.evaluationPreservesLimitsOfShape
code: noncomputable instance evaluationPreservesLimitsOfShape (X : Cᵒᵖ) :
    PreservesLimitsOfShape D (evaluation R X : SheafOfModules.{v} R ⥤ _) 
goal: CategoryTheory.Limits.PreservesLimitsOfShape D (SheafOfModules.evaluation R X)

full_name: SheafOfModules.forgetPreservesLimitsOfShape
code: noncomputable instance forgetPreservesLimitsOfShape :
    PreservesLimitsOfShape D (forget.{v} R) 
goal: CategoryTheory.Limits.PreservesLimitsOfShape D (SheafOfModules.forget R)

full_name: SheafOfModules.Finite.hasFiniteLimits
code: instance hasFiniteLimits : HasFiniteLimits (SheafOfModules.{v} R) 
goal: CategoryTheory.Limits.HasFiniteLimits (SheafOfModules R)

full_name: SheafOfModules.Finite.evaluationPreservesFiniteLimits
code: noncomputable instance evaluationPreservesFiniteLimits (X : Cᵒᵖ) :
    PreservesFiniteLimits (evaluation.{v} R X) 
goal: CategoryTheory.Limits.PreservesFiniteLimits (SheafOfModules.evaluation R X)

full_name: SheafOfModules.Finite.forgetPreservesFiniteLimits
code: noncomputable instance forgetPreservesFiniteLimits :
    PreservesFiniteLimits (forget.{v} R) 
goal: CategoryTheory.Limits.PreservesFiniteLimits (SheafOfModules.forget R)

full_name: SheafOfModules.hasLimitsOfSize
code: instance hasLimitsOfSize : HasLimitsOfSize.{v₂, v} (SheafOfModules.{v} R) 
goal: CategoryTheory.Limits.HasLimitsOfSize.{v₂, v, max u₁ v, max (max (max (v + 1) u) u₁) v₁} (SheafOfModules R)

full_name: SheafOfModules.evaluationPreservesLimitsOfSize
code: noncomputable instance evaluationPreservesLimitsOfSize (X : Cᵒᵖ) :
    PreservesLimitsOfSize.{v₂, v} (evaluation R X : SheafOfModules.{v} R ⥤ _) 
goal: CategoryTheory.Limits.PreservesLimitsOfSize.{v₂, v, max u₁ v, v, max (max (max u u₁) (v + 1)) v₁, max u (v + 1)}
  (SheafOfModules.evaluation R X)

full_name: SheafOfModules.forgetPreservesLimitsOfSize
code: noncomputable instance forgetPreservesLimitsOfSize :
    PreservesLimitsOfSize.{v₂, v} (forget.{v} R) 
goal: CategoryTheory.Limits.PreservesLimitsOfSize.{v₂, v, max u₁ v, max u₁ v, max (max (max u u₁) (v + 1)) v₁,
    max (max (max u u₁) (v + 1)) v₁}
  (SheafOfModules.forget R)

full_name: SheafOfModules.instPreservesFiniteLimitsFunctorOppositeAddCommGrpCompSheafToSheafSheafToPresheaf
code: noncomputable instance :
     PreservesFiniteLimits (SheafOfModules.toSheaf.{v} R ⋙ sheafToPresheaf _ _) 
goal: CategoryTheory.Limits.PreservesFiniteLimits (SheafOfModules.toSheaf R ⋙ CategoryTheory.sheafToPresheaf J AddCommGrp)

full_name: SheafOfModules.instPreservesFiniteLimitsSheafAddCommGrpToSheaf
code: noncomputable instance : PreservesFiniteLimits (SheafOfModules.toSheaf.{v} R) 
goal: CategoryTheory.Limits.PreservesFiniteLimits (SheafOfModules.toSheaf R)