File: Mathlib/Condensed/Light/Explicit.lean

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

full_name: LightCondensed.ofSheafLightProfinite_val
code: /--
The light condensed object associated to a presheaf on `LightProfinite` which preserves finite
products and satisfies the equalizer condition.
-/
@[simps]
noncomputable def ofSheafLightProfinite (F : LightProfinite.{u}ᵒᵖ ⥤ A) [PreservesFiniteProducts F]
    (hF : EqualizerCondition F) : LightCondensed A 
goal: (LightCondensed.ofSheafLightProfinite F hF).val = F

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

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

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

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

full_name: LightCondSet.ofSheafLightProfinite
code: /-- A `LightCondSet` version of `LightCondensed.ofSheafLightProfinite`. -/
noncomputable abbrev ofSheafLightProfinite (F : LightProfinite.{u}ᵒᵖ ⥤ Type u)
    [PreservesFiniteProducts F] (hF : EqualizerCondition F) : LightCondSet 
goal: LightCondSet

full_name: LightCondMod.ofSheafLightProfinite
code: /-- A `LightCondAb` version of `LightCondensed.ofSheafLightProfinite`. -/
noncomputable abbrev ofSheafLightProfinite (F : LightProfinite.{u}ᵒᵖ ⥤ ModuleCat.{u} R)
    [PreservesFiniteProducts F] (hF : EqualizerCondition F) : LightCondMod.{u} R 
goal: LightCondMod R

full_name: LightCondAb.ofSheafLightProfinite
code: /-- A `LightCondAb` version of `LightCondensed.ofSheafLightProfinite`. -/
noncomputable abbrev ofSheafLightProfinite (F : LightProfiniteᵒᵖ ⥤ ModuleCat ℤ)
    [PreservesFiniteProducts F] (hF : EqualizerCondition F) : LightCondAb 
goal: LightCondAb