File: Mathlib/CategoryTheory/Preadditive/EilenbergMoore.lean

full_name: CategoryTheory.Monad.algebraPreadditive_homGroup_add_f
code: /-- The category of algebras over an additive monad on a preadditive category is preadditive. -/
@[simps]
instance Monad.algebraPreadditive : Preadditive (Monad.Algebra T) 
goal: (α + β).f = α.f + β.f

full_name: CategoryTheory.Monad.algebraPreadditive_homGroup_zsmul_f
code: /-- The category of algebras over an additive monad on a preadditive category is preadditive. -/
@[simps]
instance Monad.algebraPreadditive : Preadditive (Monad.Algebra T) 
goal: (r • α).f = r • α.f

full_name: CategoryTheory.Monad.algebraPreadditive
code: /-- The category of algebras over an additive monad on a preadditive category is preadditive. -/
@[simps]
instance Monad.algebraPreadditive : Preadditive (Monad.Algebra T) 
goal: CategoryTheory.Preadditive T.Algebra

full_name: CategoryTheory.Monad.algebraPreadditive_homGroup_zero_f
code: /-- The category of algebras over an additive monad on a preadditive category is preadditive. -/
@[simps]
instance Monad.algebraPreadditive : Preadditive (Monad.Algebra T) 
goal: CategoryTheory.Monad.Algebra.Hom.f 0 = 0

full_name: CategoryTheory.Monad.algebraPreadditive_homGroup_nsmul_f
code: /-- The category of algebras over an additive monad on a preadditive category is preadditive. -/
@[simps]
instance Monad.algebraPreadditive : Preadditive (Monad.Algebra T) 
goal: (n • α).f = n • α.f

full_name: CategoryTheory.Monad.algebraPreadditive_homGroup_neg_f
code: /-- The category of algebras over an additive monad on a preadditive category is preadditive. -/
@[simps]
instance Monad.algebraPreadditive : Preadditive (Monad.Algebra T) 
goal: (-α).f = -α.f

full_name: CategoryTheory.Monad.algebraPreadditive_homGroup_sub_f
code: /-- The category of algebras over an additive monad on a preadditive category is preadditive. -/
@[simps]
instance Monad.algebraPreadditive : Preadditive (Monad.Algebra T) 
goal: (α - β).f = α.f - β.f

full_name: CategoryTheory.Monad.forget_additive
code: instance Monad.forget_additive : (Monad.forget T).Additive 
goal: T.forget.Additive

full_name: CategoryTheory.Comonad.coalgebraPreadditive
code: /-- The category of coalgebras over an additive comonad on a preadditive category is preadditive. -/
@[simps]
instance Comonad.coalgebraPreadditive : Preadditive (Comonad.Coalgebra U) 
goal: CategoryTheory.Preadditive U.Coalgebra

full_name: CategoryTheory.Comonad.coalgebraPreadditive_homGroup_nsmul_f
code: /-- The category of coalgebras over an additive comonad on a preadditive category is preadditive. -/
@[simps]
instance Comonad.coalgebraPreadditive : Preadditive (Comonad.Coalgebra U) 
goal: (n • α).f = n • α.f

full_name: CategoryTheory.Comonad.coalgebraPreadditive_homGroup_zero_f
code: /-- The category of coalgebras over an additive comonad on a preadditive category is preadditive. -/
@[simps]
instance Comonad.coalgebraPreadditive : Preadditive (Comonad.Coalgebra U) 
goal: CategoryTheory.Comonad.Coalgebra.Hom.f 0 = 0

full_name: CategoryTheory.Comonad.coalgebraPreadditive_homGroup_neg_f
code: /-- The category of coalgebras over an additive comonad on a preadditive category is preadditive. -/
@[simps]
instance Comonad.coalgebraPreadditive : Preadditive (Comonad.Coalgebra U) 
goal: (-α).f = -α.f

full_name: CategoryTheory.Comonad.coalgebraPreadditive_homGroup_zsmul_f
code: /-- The category of coalgebras over an additive comonad on a preadditive category is preadditive. -/
@[simps]
instance Comonad.coalgebraPreadditive : Preadditive (Comonad.Coalgebra U) 
goal: (r • α).f = r • α.f

full_name: CategoryTheory.Comonad.coalgebraPreadditive_homGroup_add_f
code: /-- The category of coalgebras over an additive comonad on a preadditive category is preadditive. -/
@[simps]
instance Comonad.coalgebraPreadditive : Preadditive (Comonad.Coalgebra U) 
goal: (α + β).f = α.f + β.f

full_name: CategoryTheory.Comonad.coalgebraPreadditive_homGroup_sub_f
code: /-- The category of coalgebras over an additive comonad on a preadditive category is preadditive. -/
@[simps]
instance Comonad.coalgebraPreadditive : Preadditive (Comonad.Coalgebra U) 
goal: (α - β).f = α.f - β.f

full_name: CategoryTheory.Comonad.forget_additive
code: instance Comonad.forget_additive : (Comonad.forget U).Additive 
goal: U.forget.Additive