File: Mathlib/Condensed/Explicit.lean

full_name: Condensed.ofSheafStonean
code: /-- The condensed object associated to a finite-product-preserving presheaf on `Stonean`. -/
noncomputable def ofSheafStonean
    [∀ X, HasLimitsOfShape (StructuredArrow X Stonean.toCompHaus.op) A]
    (F : Stonean.{u}ᵒᵖ ⥤ A) [PreservesFiniteProducts F] :
    Condensed A 
goal: Condensed A

full_name: Condensed.ofSheafForgetStonean
code: /--
The condensed object associated to a presheaf on `Stonean` whose postcomposition with the
forgetful functor preserves finite products.
-/
noncomputable def ofSheafForgetStonean
    [∀ X, HasLimitsOfShape (StructuredArrow X Stonean.toCompHaus.op) A]
    [ConcreteCategory A] [ReflectsFiniteProducts (CategoryTheory.forget A)]
    (F : Stonean.{u}ᵒᵖ ⥤ A) [PreservesFiniteProducts (F ⋙ CategoryTheory.forget A)] :
    Condensed A 
goal: Condensed A

full_name: Condensed.ofSheafProfinite
code: /--
The condensed object associated to a presheaf on `Profinite` which preserves finite products and
satisfies the equalizer condition.
-/
noncomputable def ofSheafProfinite
    [∀ X, HasLimitsOfShape (StructuredArrow X profiniteToCompHaus.op) A]
    (F : Profinite.{u}ᵒᵖ ⥤ A) [PreservesFiniteProducts F]
    (hF : EqualizerCondition F) : Condensed A 
goal: Condensed A

full_name: Condensed.ofSheafForgetProfinite
code: /--
The condensed object associated to a presheaf on `Profinite` whose postcomposition with the
forgetful functor preserves finite products and satisfies the equalizer condition.
-/
noncomputable def ofSheafForgetProfinite
    [∀ X, HasLimitsOfShape (StructuredArrow X profiniteToCompHaus.op) A]
    [ConcreteCategory A] [ReflectsFiniteLimits (CategoryTheory.forget A)]
    (F : Profinite.{u}ᵒᵖ ⥤ A) [PreservesFiniteProducts (F ⋙ CategoryTheory.forget A)]
    (hF : EqualizerCondition (F ⋙ CategoryTheory.forget A)) :
    Condensed A 
goal: Condensed A

full_name: Condensed.ofSheafCompHaus
code: /--
The condensed object associated to a presheaf on `CompHaus` which preserves finite products and
satisfies the equalizer condition.
-/
noncomputable def ofSheafCompHaus
    (F : CompHaus.{u}ᵒᵖ ⥤ A) [PreservesFiniteProducts F]
    (hF : EqualizerCondition F) : Condensed A 
goal: Condensed A

full_name: Condensed.ofSheafForgetCompHaus
code: /--
The condensed object associated to a presheaf on `CompHaus` whose postcomposition with the
forgetful functor preserves finite products and satisfies the equalizer condition.
-/
noncomputable def ofSheafForgetCompHaus
    [ConcreteCategory A] [ReflectsFiniteLimits (CategoryTheory.forget A)]
    (F : CompHaus.{u}ᵒᵖ ⥤ A) [PreservesFiniteProducts (F ⋙ CategoryTheory.forget A)]
    (hF : EqualizerCondition (F ⋙ CategoryTheory.forget A)) : Condensed A 
goal: Condensed A

full_name: Condensed.equalizerCondition
code: /-- A condensed object satisfies the equalizer condition. -/
theorem equalizerCondition (X : Condensed A) : EqualizerCondition X.val 
goal: CategoryTheory.regularTopology.EqualizerCondition X.val

full_name: Condensed.instPreservesFiniteProductsOppositeCompHausVal
code: /-- A condensed object preserves finite products. -/
noncomputable instance (X : Condensed A) : PreservesFiniteProducts X.val 
goal: CategoryTheory.Limits.PreservesFiniteProducts X.val

full_name: Condensed.instPreservesFiniteProductsOppositeProfiniteVal
code: /-- A condensed object regarded as a sheaf on `Profinite` preserves finite products. -/
noncomputable instance (X : Sheaf (coherentTopology Profinite.{u}) A) :
    PreservesFiniteProducts X.val 
goal: CategoryTheory.Limits.PreservesFiniteProducts X.val

full_name: Condensed.equalizerCondition_profinite
code: /-- A condensed object regarded as a sheaf on `Profinite` satisfies the equalizer condition. -/
theorem equalizerCondition_profinite (X : Sheaf (coherentTopology Profinite.{u}) A) :
    EqualizerCondition X.val 
goal: CategoryTheory.regularTopology.EqualizerCondition X.val

full_name: Condensed.instPreservesFiniteProductsOppositeStoneanVal
code: /-- A condensed object regarded as a sheaf on `Stonean` preserves finite products. -/
noncomputable instance (X : Sheaf (coherentTopology Stonean.{u}) A) :
    PreservesFiniteProducts X.val 
goal: CategoryTheory.Limits.PreservesFiniteProducts X.val

full_name: CondensedSet.ofSheafStonean
code: /-- A `CondensedSet` version of `Condensed.ofSheafStonean`. -/
noncomputable abbrev ofSheafStonean (F : Stonean.{u}ᵒᵖ ⥤ Type (u+1)) [PreservesFiniteProducts F] :
    CondensedSet 
goal: CondensedSet

full_name: CondensedSet.ofSheafProfinite
code: /-- A `CondensedSet` version of `Condensed.ofSheafProfinite`. -/
noncomputable abbrev ofSheafProfinite (F : Profinite.{u}ᵒᵖ ⥤ Type (u+1))
    [PreservesFiniteProducts F] (hF : EqualizerCondition F) : CondensedSet 
goal: CondensedSet

full_name: CondensedSet.ofSheafCompHaus
code: /-- A `CondensedSet` version of `Condensed.ofSheafCompHaus`. -/
noncomputable abbrev ofSheafCompHaus (F : CompHaus.{u}ᵒᵖ ⥤ Type (u+1))
    [PreservesFiniteProducts F] (hF : EqualizerCondition F) : CondensedSet 
goal: CondensedSet

full_name: CondensedMod.ofSheafStonean
code: /-- A `CondensedMod` version of `Condensed.ofSheafStonean`. -/
noncomputable abbrev ofSheafStonean (F : Stonean.{u}ᵒᵖ ⥤ ModuleCat.{u+1} R)
    [PreservesFiniteProducts F] : CondensedMod R 
goal: CondensedMod R

full_name: CondensedMod.ofSheafProfinite
code: /-- A `CondensedMod` version of `Condensed.ofSheafProfinite`. -/
noncomputable abbrev ofSheafProfinite (F : Profinite.{u}ᵒᵖ ⥤ ModuleCat.{u+1} R)
    [PreservesFiniteProducts F] (hF : EqualizerCondition F) : CondensedMod R 
goal: CondensedMod R

full_name: CondensedMod.ofSheafCompHaus
code: /-- A `CondensedMod` version of `Condensed.ofSheafCompHaus`. -/
noncomputable abbrev ofSheafCompHaus (F : CompHaus.{u}ᵒᵖ ⥤ ModuleCat.{u+1} R)
    [PreservesFiniteProducts F] (hF : EqualizerCondition F) : CondensedMod R 
goal: CondensedMod R