File: Mathlib/Condensed/Light/Discrete.lean

full_name: LightCondensed.discrete
code: /--
The discrete condensed object associated to an object of `C` is the constant sheaf at that object.
-/
@[simps!]
noncomputable def LightCondensed.discrete : C ⥤ LightCondensed.{u} C 
goal: C ⥤ LightCondensed C

full_name: LightCondensed.discrete_obj
code: /--
The discrete condensed object associated to an object of `C` is the constant sheaf at that object.
-/
@[simps!]
noncomputable def LightCondensed.discrete : C ⥤ LightCondensed.{u} C 
goal: (LightCondensed.discrete C).obj X =
  (CategoryTheory.presheafToSheaf (CategoryTheory.coherentTopology LightProfinite) C).obj
    ((CategoryTheory.Functor.const LightProfiniteᵒᵖ).obj X)

full_name: LightCondensed.discrete_map
code: /--
The discrete condensed object associated to an object of `C` is the constant sheaf at that object.
-/
@[simps!]
noncomputable def LightCondensed.discrete : C ⥤ LightCondensed.{u} C 
goal: ∀ {X Y : C} (f : X ⟶ Y),
  (LightCondensed.discrete C).map f =
    (CategoryTheory.presheafToSheaf (CategoryTheory.coherentTopology LightProfinite) C).map
      ((CategoryTheory.Functor.const LightProfiniteᵒᵖ).map f)

full_name: LightCondensed.underlying_obj
code: /--
The underlying object of a condensed object in `C` is the condensed object evaluated at a point.
This can be viewed as a sort of forgetful functor from `Condensed C` to `C`
-/
@[simps!]
noncomputable def LightCondensed.underlying : LightCondensed.{u} C ⥤ C 
goal: (LightCondensed.underlying C).obj j = j.val.obj (Opposite.op (LightProfinite.of PUnit.{u + 1}))

full_name: LightCondensed.underlying_map
code: /--
The underlying object of a condensed object in `C` is the condensed object evaluated at a point.
This can be viewed as a sort of forgetful functor from `Condensed C` to `C`
-/
@[simps!]
noncomputable def LightCondensed.underlying : LightCondensed.{u} C ⥤ C 
goal: ∀ {X Y : CategoryTheory.Sheaf (CategoryTheory.coherentTopology LightProfinite) C} (f : X ⟶ Y),
  (LightCondensed.underlying C).map f = f.val.app (Opposite.op (LightProfinite.of PUnit.{u + 1}))

full_name: LightCondensed.underlying
code: /--
The underlying object of a condensed object in `C` is the condensed object evaluated at a point.
This can be viewed as a sort of forgetful functor from `Condensed C` to `C`
-/
@[simps!]
noncomputable def LightCondensed.underlying : LightCondensed.{u} C ⥤ C 
goal: LightCondensed C ⥤ C

full_name: LightCondensed.discreteUnderlyingAdj
code: /--
Discreteness is left adjoint to the forgetful functor. When `C` is `Type*`, this is analogous to
`TopCat.adj₁ : TopCat.discrete ⊣ forget TopCat`.  
-/
noncomputable def LightCondensed.discreteUnderlyingAdj : discrete C ⊣ underlying C 
goal: LightCondensed.discrete C ⊣ LightCondensed.underlying C

full_name: LightCondSet.discrete
code: /-- A version of `LightCondensed.discrete` in the `LightCondSet` namespace -/
noncomputable abbrev LightCondSet.discrete 
goal: Type u ⥤ LightCondensed (Type u)

full_name: LightCondSet.underlying
code: /-- A version of `LightCondensed.underlying` in the `LightCondSet` namespace -/
noncomputable abbrev LightCondSet.underlying 
goal: LightCondensed (Type u) ⥤ Type u

full_name: LightCondSet.discreteUnderlyingAdj
code: /-- A version of `LightCondensed.discrete_underlying_adj` in the `LightCondSet` namespace -/
noncomputable abbrev LightCondSet.discreteUnderlyingAdj : discrete ⊣ underlying 
goal: LightCondSet.discrete ⊣ LightCondSet.underlying