File: Mathlib/CategoryTheory/Limits/FintypeCat.lean

full_name: CategoryTheory.Limits.FintypeCat.instFiniteObjCompFintypeCatIncl
code: instance {J : Type} [SmallCategory J] (K : J ⥤ FintypeCat.{u}) (j : J) :
    Finite ((K ⋙ FintypeCat.incl.{u}).obj j) 
goal: Finite ((K ⋙ FintypeCat.incl).obj j)

full_name: CategoryTheory.Limits.FintypeCat.finiteLimitOfFiniteDiagram
code: /-- Any functor from a finite category to Types that only involves finite objects,
has a finite limit. -/
noncomputable instance finiteLimitOfFiniteDiagram {J : Type} [SmallCategory J] [FinCategory J]
    (K : J ⥤ Type*) [∀ j, Finite (K.obj j)] : Fintype (limit K) 
goal: Fintype (CategoryTheory.Limits.limit K)

full_name: CategoryTheory.Limits.FintypeCat.inclusionCreatesFiniteLimits
code: noncomputable instance inclusionCreatesFiniteLimits {J : Type} [SmallCategory J] [FinCategory J] :
    CreatesLimitsOfShape J FintypeCat.incl.{u} 
goal: CategoryTheory.CreatesLimitsOfShape J FintypeCat.incl

full_name: CategoryTheory.Limits.FintypeCat.instCreatesLimitsOfShapeFintypeCatForgetOfFinCategory
code: noncomputable instance {J : Type} [SmallCategory J] [FinCategory J] :
    CreatesLimitsOfShape J (forget FintypeCat) 
goal: CategoryTheory.CreatesLimitsOfShape J (CategoryTheory.forget FintypeCat)

full_name: CategoryTheory.Limits.FintypeCat.instHasLimitsOfShapeFintypeCatOfFinCategory
code: instance {J : Type} [SmallCategory J] [FinCategory J] : HasLimitsOfShape J FintypeCat.{u} 
goal: CategoryTheory.Limits.HasLimitsOfShape J FintypeCat

full_name: CategoryTheory.Limits.FintypeCat.hasFiniteLimits
code: instance hasFiniteLimits : HasFiniteLimits FintypeCat.{u} 
goal: CategoryTheory.Limits.HasFiniteLimits FintypeCat

full_name: CategoryTheory.Limits.FintypeCat.inclusionPreservesFiniteLimits
code: noncomputable instance inclusionPreservesFiniteLimits :
    PreservesFiniteLimits FintypeCat.incl.{u} 
goal: CategoryTheory.Limits.PreservesFiniteLimits FintypeCat.incl

full_name: CategoryTheory.Limits.FintypeCat.instPreservesFiniteLimitsFintypeCatForget
code: noncomputable instance : PreservesFiniteLimits (forget FintypeCat) 
goal: CategoryTheory.Limits.PreservesFiniteLimits (CategoryTheory.forget FintypeCat)

full_name: CategoryTheory.Limits.FintypeCat.finiteColimitOfFiniteDiagram
code: /-- Any functor from a finite category to Types that only involves finite objects,
has a finite colimit. -/
noncomputable instance finiteColimitOfFiniteDiagram {J : Type} [SmallCategory J] [FinCategory J]
    (K : J ⥤ Type*) [∀ j, Finite (K.obj j)] : Fintype (colimit K) 
goal: Fintype (CategoryTheory.Limits.colimit K)

full_name: CategoryTheory.Limits.FintypeCat.inclusionCreatesFiniteColimits
code: noncomputable instance inclusionCreatesFiniteColimits {J : Type} [SmallCategory J] [FinCategory J] :
    CreatesColimitsOfShape J FintypeCat.incl.{u} 
goal: CategoryTheory.CreatesColimitsOfShape J FintypeCat.incl

full_name: CategoryTheory.Limits.FintypeCat.instCreatesColimitsOfShapeFintypeCatForgetOfFinCategory
code: noncomputable instance {J : Type} [SmallCategory J] [FinCategory J] :
    CreatesColimitsOfShape J (forget FintypeCat) 
goal: CategoryTheory.CreatesColimitsOfShape J (CategoryTheory.forget FintypeCat)

full_name: CategoryTheory.Limits.FintypeCat.instHasColimitsOfShapeFintypeCatOfFinCategory
code: instance {J : Type} [SmallCategory J] [FinCategory J] : HasColimitsOfShape J FintypeCat.{u} 
goal: CategoryTheory.Limits.HasColimitsOfShape J FintypeCat

full_name: CategoryTheory.Limits.FintypeCat.hasFiniteColimits
code: instance hasFiniteColimits : HasFiniteColimits FintypeCat.{u} 
goal: CategoryTheory.Limits.HasFiniteColimits FintypeCat

full_name: CategoryTheory.Limits.FintypeCat.inclusionPreservesFiniteColimits
code: noncomputable instance inclusionPreservesFiniteColimits :
    PreservesFiniteColimits FintypeCat.incl.{u} 
goal: CategoryTheory.Limits.PreservesFiniteColimits FintypeCat.incl

full_name: CategoryTheory.Limits.FintypeCat.instPreservesFiniteColimitsFintypeCatForget
code: noncomputable instance : PreservesFiniteColimits (forget FintypeCat) 
goal: CategoryTheory.Limits.PreservesFiniteColimits (CategoryTheory.forget FintypeCat)