File: Mathlib/Algebra/Category/ModuleCat/Colimits.lean

full_name: ModuleCat.HasColimit.coconePointSMul
code: /-- The induced scalar multiplication on
`colimit (F ⋙ forget₂ _ AddCommGrp)`. -/
@[simps]
noncomputable def coconePointSMul :
    R →+* End (colimit (F ⋙ forget₂ _ AddCommGrp)) 
goal: R →+* CategoryTheory.End (CategoryTheory.Limits.colimit (F ⋙ CategoryTheory.forget₂ (ModuleCat R) AddCommGrp))

full_name: ModuleCat.HasColimit.coconePointSMul_apply
code: /-- The induced scalar multiplication on
`colimit (F ⋙ forget₂ _ AddCommGrp)`. -/
@[simps]
noncomputable def coconePointSMul :
    R →+* End (colimit (F ⋙ forget₂ _ AddCommGrp)) 
goal: (ModuleCat.HasColimit.coconePointSMul F) r =
  CategoryTheory.Limits.colimMap { app := fun j => (F.obj j).smul r, naturality := ⋯ }

full_name: ModuleCat.HasColimit.colimitCocone
code: /-- The cocone for `F` constructed from the colimit of
`(F ⋙ forget₂ (ModuleCat R) AddCommGrp)`. -/
@[simps]
noncomputable def colimitCocone : Cocone F 
goal: CategoryTheory.Limits.Cocone F

full_name: ModuleCat.HasColimit.colimitCocone_pt
code: /-- The cocone for `F` constructed from the colimit of
`(F ⋙ forget₂ (ModuleCat R) AddCommGrp)`. -/
@[simps]
noncomputable def colimitCocone : Cocone F 
goal: (ModuleCat.HasColimit.colimitCocone F).pt = ModuleCat.mkOfSMul (ModuleCat.HasColimit.coconePointSMul F)

full_name: ModuleCat.HasColimit.colimitCocone_ι_app
code: /-- The cocone for `F` constructed from the colimit of
`(F ⋙ forget₂ (ModuleCat R) AddCommGrp)`. -/
@[simps]
noncomputable def colimitCocone : Cocone F 
goal: (ModuleCat.HasColimit.colimitCocone F).ι.app j =
  ModuleCat.homMk (CategoryTheory.Limits.colimit.ι (F ⋙ CategoryTheory.forget₂ (ModuleCat R) AddCommGrp) j) ⋯

full_name: ModuleCat.HasColimit.isColimitColimitCocone
code: /-- The cocone for `F` constructed from the colimit of
`(F ⋙ forget₂ (ModuleCat R) AddCommGrp)` is a colimit cocone. -/
noncomputable def isColimitColimitCocone : IsColimit (colimitCocone F) 
goal: CategoryTheory.Limits.IsColimit (ModuleCat.HasColimit.colimitCocone F)

full_name: ModuleCat.HasColimit.instHasColimit
code: instance : HasColimit F 
goal: CategoryTheory.Limits.HasColimit F

full_name: ModuleCat.HasColimit.instPreservesColimitAddCommGrpForget₂
code: noncomputable instance : PreservesColimit F (forget₂ _ AddCommGrp) 
goal: CategoryTheory.Limits.PreservesColimit F (CategoryTheory.forget₂ (ModuleCat R) AddCommGrp)

full_name: ModuleCat.HasColimit.reflectsColimit
code: noncomputable instance reflectsColimit :
    ReflectsColimit F (forget₂ (ModuleCat.{w'} R) AddCommGrp) 
goal: CategoryTheory.Limits.ReflectsColimit F (CategoryTheory.forget₂ (ModuleCat R) AddCommGrp)

full_name: ModuleCat.hasColimitsOfShape
code: instance hasColimitsOfShape [HasColimitsOfShape J AddCommGrp.{w'}] :
    HasColimitsOfShape J (ModuleCat.{w'} R) 
goal: CategoryTheory.Limits.HasColimitsOfShape J (ModuleCat R)

full_name: ModuleCat.reflectsColimitsOfShape
code: noncomputable instance reflectsColimitsOfShape [HasColimitsOfShape J AddCommGrp.{w'}] :
    ReflectsColimitsOfShape J (forget₂ (ModuleCat.{w'} R) AddCommGrp) 
goal: CategoryTheory.Limits.ReflectsColimitsOfShape J (CategoryTheory.forget₂ (ModuleCat R) AddCommGrp)

full_name: ModuleCat.hasColimitsOfSize
code: instance hasColimitsOfSize [HasColimitsOfSize.{v, u} AddCommGrp.{w'}] :
    HasColimitsOfSize.{v, u} (ModuleCat.{w'} R) 
goal: CategoryTheory.Limits.HasColimitsOfSize.{v, u, w', max (w' + 1) w} (ModuleCat R)

full_name: ModuleCat.forget₂PreservesColimitsOfShape
code: noncomputable instance forget₂PreservesColimitsOfShape
    [HasColimitsOfShape J AddCommGrp.{w'}] :
    PreservesColimitsOfShape J (forget₂ (ModuleCat.{w'} R) AddCommGrp) 
goal: CategoryTheory.Limits.PreservesColimitsOfShape J (CategoryTheory.forget₂ (ModuleCat R) AddCommGrp)

full_name: ModuleCat.forget₂PreservesColimitsOfSize
code: noncomputable instance forget₂PreservesColimitsOfSize
    [HasColimitsOfSize.{u, v} AddCommGrp.{w'}] :
    PreservesColimitsOfSize.{u, v} (forget₂ (ModuleCat.{w'} R) AddCommGrp) 
goal: CategoryTheory.Limits.PreservesColimitsOfSize.{u, v, w', w', max w (w' + 1), w' + 1}
  (CategoryTheory.forget₂ (ModuleCat R) AddCommGrp)

full_name: ModuleCat.instPreservesColimitsOfSizeModuleCatMaxAddCommGrpForget₂OfHasColimitsOfSizeAddCommGrpMax
code: noncomputable instance
    [HasColimitsOfSize.{u, v} AddCommGrpMax.{w, w'}] :
    PreservesColimitsOfSize.{u, v} (forget₂ (ModuleCatMax.{w, w'} R) AddCommGrp) 
goal: CategoryTheory.Limits.PreservesColimitsOfSize.{u, v, max w w', max w w', max (w + 1) (w' + 1), max (w + 1) (w' + 1)}
  (CategoryTheory.forget₂ (ModuleCatMax R) AddCommGrp)

full_name: ModuleCat.instHasFiniteColimits
code: instance : HasFiniteColimits (ModuleCat.{w'} R) 
goal: CategoryTheory.Limits.HasFiniteColimits (ModuleCat R)

full_name: ModuleCat.instHasCoequalizers
code: instance : HasCoequalizers (ModuleCat.{v} R) 
goal: CategoryTheory.Limits.HasCoequalizers (ModuleCat R)