File: Mathlib/CategoryTheory/Preadditive/EndoFunctor.lean

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

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

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

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

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

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

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

full_name: CategoryTheory.Algebra.forget_additive
code: instance Algebra.forget_additive : (Endofunctor.Algebra.forget F).Additive 
goal: (CategoryTheory.Endofunctor.Algebra.forget F).Additive

full_name: CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_add_f
code: @[simps]
instance Endofunctor.coalgebraPreadditive : Preadditive (Endofunctor.Coalgebra F) 
goal: (α + β).f = α.f + β.f

full_name: CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_sub_f
code: @[simps]
instance Endofunctor.coalgebraPreadditive : Preadditive (Endofunctor.Coalgebra F) 
goal: (α - β).f = α.f - β.f

full_name: CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_zero_f
code: @[simps]
instance Endofunctor.coalgebraPreadditive : Preadditive (Endofunctor.Coalgebra F) 
goal: CategoryTheory.Endofunctor.Coalgebra.Hom.f 0 = 0

full_name: CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_nsmul_f
code: @[simps]
instance Endofunctor.coalgebraPreadditive : Preadditive (Endofunctor.Coalgebra F) 
goal: (n • α).f = n • α.f

full_name: CategoryTheory.Endofunctor.coalgebraPreadditive
code: @[simps]
instance Endofunctor.coalgebraPreadditive : Preadditive (Endofunctor.Coalgebra F) 
goal: CategoryTheory.Preadditive (CategoryTheory.Endofunctor.Coalgebra F)

full_name: CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_neg_f
code: @[simps]
instance Endofunctor.coalgebraPreadditive : Preadditive (Endofunctor.Coalgebra F) 
goal: (-α).f = -α.f

full_name: CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_zsmul_f
code: @[simps]
instance Endofunctor.coalgebraPreadditive : Preadditive (Endofunctor.Coalgebra F) 
goal: (r • α).f = r • α.f

full_name: CategoryTheory.Coalgebra.forget_additive
code: instance Coalgebra.forget_additive : (Endofunctor.Coalgebra.forget F).Additive 
goal: (CategoryTheory.Endofunctor.Coalgebra.forget F).Additive