Math.FiniteCategories.FullSubcategory

Selecting a FullSubcategory in a Category yields a FiniteCategory.

We have to forget the generating set of morphisms of the original Category as the generators are not always inheritable (see for example the full subcategory of Square containing the objects A and D).

If the generators are inheritable, you can use the constructor InheritedFullSubcategory to inherit the generators of the original Category.

Documentation

data FullSubcategory c m o

A FullSubcategory needs an original category and a set of objects to select in the category.

The generators are forgotten, use InheritedFullSubcategory if the generators are inheritable.

Constructors

FullSubcategory c (Set o)

Instances

(Eq c, Eq o) => Eq (FullSubcategory c m o)

Defined in Math.FiniteCategories.FullSubcategory

Methods

(==) :: FullSubcategory c m o -> FullSubcategory c m o -> Bool

(/=) :: FullSubcategory c m o -> FullSubcategory c m o -> Bool

(Show c, Show o) => Show (FullSubcategory c m o)

Defined in Math.FiniteCategories.FullSubcategory

Methods

showsPrec :: Int -> FullSubcategory c m o -> ShowS

show :: FullSubcategory c m o -> String

showList :: [FullSubcategory c m o] -> ShowS

(PrettyPrint c, PrettyPrint m, PrettyPrint o, Eq o) => PrettyPrint (FullSubcategory c m o)

Defined in Math.FiniteCategories.FullSubcategory

Methods

pprint :: FullSubcategory c m o -> String

(Category c m o, Eq o) => Category (FullSubcategory c m o) m o

Defined in Math.FiniteCategories.FullSubcategory

Methods

identity :: FullSubcategory c m o -> o -> m

ar :: FullSubcategory c m o -> o -> o -> Set m

genAr :: FullSubcategory c m o -> o -> o -> Set m

decompose :: FullSubcategory c m o -> m -> [m]

(Category c m o, Eq o) => FiniteCategory (FullSubcategory c m o) m o

Defined in Math.FiniteCategories.FullSubcategory

Methods

ob :: FullSubcategory c m o -> Set o

data InheritedFullSubcategory c m o

An InheritedFullSubcategory is a FullSubcategory where the generators are the same as in the original Category.

Constructors

InheritedFullSubcategory c (Set o)

Instances

(Eq c, Eq o) => Eq (InheritedFullSubcategory c m o)

Defined in Math.FiniteCategories.FullSubcategory

Methods

(==) :: InheritedFullSubcategory c m o -> InheritedFullSubcategory c m o -> Bool

(/=) :: InheritedFullSubcategory c m o -> InheritedFullSubcategory c m o -> Bool

(Show c, Show o) => Show (InheritedFullSubcategory c m o)

Defined in Math.FiniteCategories.FullSubcategory

Methods

showsPrec :: Int -> InheritedFullSubcategory c m o -> ShowS

show :: InheritedFullSubcategory c m o -> String

showList :: [InheritedFullSubcategory c m o] -> ShowS

(PrettyPrint c, PrettyPrint m, PrettyPrint o, Eq o) => PrettyPrint (InheritedFullSubcategory c m o)

Defined in Math.FiniteCategories.FullSubcategory

Methods

pprint :: InheritedFullSubcategory c m o -> String

(Category c m o, Eq o) => Category (InheritedFullSubcategory c m o) m o

Defined in Math.FiniteCategories.FullSubcategory

Methods

identity :: InheritedFullSubcategory c m o -> o -> m

ar :: InheritedFullSubcategory c m o -> o -> o -> Set m

genAr :: InheritedFullSubcategory c m o -> o -> o -> Set m

decompose :: InheritedFullSubcategory c m o -> m -> [m]

(Category c m o, Eq o) => FiniteCategory (InheritedFullSubcategory c m o) m o

Defined in Math.FiniteCategories.FullSubcategory

Methods

ob :: InheritedFullSubcategory c m o -> Set o