File: Mathlib/Algebra/Category/Grp/EquivalenceGroupAddGroup.lean

full_name: _private.Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup.0.Grp.instMulOneClassαGroup
code: private instance (X : Grp) : MulOneClass X.α 
goal: MulOneClass ↑X

full_name: _private.Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup.0.Grp.instMulOneClassαCommGroup
code: private instance (X : CommGrp) : MulOneClass X.α 
goal: MulOneClass ↑X

full_name: _private.Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup.0.Grp.instAddZeroClassαAddGroup
code: private instance (X : AddGrp) : AddZeroClass X.α 
goal: AddZeroClass ↑X

full_name: _private.Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup.0.Grp.instAddZeroClassαAddCommGroup
code: private instance (X : AddCommGrp) : AddZeroClass X.α 
goal: AddZeroClass ↑X

full_name: Grp.toAddGrp_obj
code: /-- The functor `Group ⥤ AddGroup` by sending `X ↦ additive X` and `f ↦ f`.
-/
@[simps]
def toAddGrp : Grp ⥤ AddGrp 
goal: Grp.toAddGrp.obj X = AddGrp.of (Additive ↑X)

full_name: Grp.toAddGrp
code: /-- The functor `Group ⥤ AddGroup` by sending `X ↦ additive X` and `f ↦ f`.
-/
@[simps]
def toAddGrp : Grp ⥤ AddGrp 
goal: Grp ⥤ AddGrp

full_name: Grp.toAddGrp_map
code: /-- The functor `Group ⥤ AddGroup` by sending `X ↦ additive X` and `f ↦ f`.
-/
@[simps]
def toAddGrp : Grp ⥤ AddGrp 
goal: Grp.toAddGrp.map a = MonoidHom.toAdditive a

full_name: CommGrp.toAddCommGrp_obj
code: /-- The functor `CommGroup ⥤ AddCommGroup` by sending `X ↦ additive X` and `f ↦ f`.
-/
@[simps]
def toAddCommGrp : CommGrp ⥤ AddCommGrp 
goal: CommGrp.toAddCommGrp.obj X = AddCommGrp.of (Additive ↑X)

full_name: CommGrp.toAddCommGrp_map
code: /-- The functor `CommGroup ⥤ AddCommGroup` by sending `X ↦ additive X` and `f ↦ f`.
-/
@[simps]
def toAddCommGrp : CommGrp ⥤ AddCommGrp 
goal: CommGrp.toAddCommGrp.map a = MonoidHom.toAdditive a

full_name: CommGrp.toAddCommGrp
code: /-- The functor `CommGroup ⥤ AddCommGroup` by sending `X ↦ additive X` and `f ↦ f`.
-/
@[simps]
def toAddCommGrp : CommGrp ⥤ AddCommGrp 
goal: CommGrp ⥤ AddCommGrp

full_name: AddGrp.toGrp_map
code: /-- The functor `AddGroup ⥤ Group` by sending `X ↦ multiplicative Y` and `f ↦ f`.
-/
@[simps]
def toGrp : AddGrp ⥤ Grp 
goal: AddGrp.toGrp.map a = AddMonoidHom.toMultiplicative a

full_name: AddGrp.toGrp
code: /-- The functor `AddGroup ⥤ Group` by sending `X ↦ multiplicative Y` and `f ↦ f`.
-/
@[simps]
def toGrp : AddGrp ⥤ Grp 
goal: AddGrp ⥤ Grp

full_name: AddGrp.toGrp_obj
code: /-- The functor `AddGroup ⥤ Group` by sending `X ↦ multiplicative Y` and `f ↦ f`.
-/
@[simps]
def toGrp : AddGrp ⥤ Grp 
goal: AddGrp.toGrp.obj X = Grp.of (Multiplicative ↑X)

full_name: AddCommGrp.toCommGrp_obj
code: /-- The functor `AddCommGroup ⥤ CommGroup` by sending `X ↦ multiplicative Y` and `f ↦ f`.
-/
@[simps]
def toCommGrp : AddCommGrp ⥤ CommGrp 
goal: AddCommGrp.toCommGrp.obj X = CommGrp.of (Multiplicative ↑X)

full_name: AddCommGrp.toCommGrp_map
code: /-- The functor `AddCommGroup ⥤ CommGroup` by sending `X ↦ multiplicative Y` and `f ↦ f`.
-/
@[simps]
def toCommGrp : AddCommGrp ⥤ CommGrp 
goal: AddCommGrp.toCommGrp.map a = AddMonoidHom.toMultiplicative a

full_name: AddCommGrp.toCommGrp
code: /-- The functor `AddCommGroup ⥤ CommGroup` by sending `X ↦ multiplicative Y` and `f ↦ f`.
-/
@[simps]
def toCommGrp : AddCommGrp ⥤ CommGrp 
goal: AddCommGrp ⥤ CommGrp

full_name: groupAddGroupEquivalence
code: /-- The equivalence of categories between `Group` and `AddGroup`
-/
def groupAddGroupEquivalence : Grp ≌ AddGrp 
goal: Grp ≌ AddGrp

full_name: commGroupAddCommGroupEquivalence
code: /-- The equivalence of categories between `CommGroup` and `AddCommGroup`.
-/
def commGroupAddCommGroupEquivalence : CommGrp ≌ AddCommGrp 
goal: CommGrp ≌ AddCommGrp