Copyright | Guillaume Sabbagh 2022 |
---|---|
License | GPL-3 |
Maintainer | guillaumesabbagh@protonmail.com |
Stability | experimental |
Portability | portable |
Safe Haskell | Safe-Inferred |
Language | Haskell2010 |
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
.
Synopsis
- data FullSubcategory c m o = FullSubcategory c (Set o)
- data InheritedFullSubcategory c m o = InheritedFullSubcategory c (Set o)
Documentation
data FullSubcategory c m o Source #
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.
FullSubcategory c (Set o) |
Instances
(PrettyPrint c, PrettyPrint o, Eq o) => PrettyPrint (FullSubcategory c m o) Source # | |
Defined in Math.FiniteCategories.FullSubcategory pprint :: Int -> FullSubcategory c m o -> String Source # pprintWithIndentations :: Int -> Int -> String -> FullSubcategory c m o -> String Source # pprintIndent :: Int -> FullSubcategory c m o -> String Source # | |
(Simplifiable c, Simplifiable o, Eq o) => Simplifiable (FullSubcategory c m o) Source # | |
Defined in Math.FiniteCategories.FullSubcategory simplify :: FullSubcategory c m o -> FullSubcategory c m o # | |
Generic (FullSubcategory c m o) Source # | |
Defined in Math.FiniteCategories.FullSubcategory type Rep (FullSubcategory c m o) :: Type -> Type from :: FullSubcategory c m o -> Rep (FullSubcategory c m o) x to :: Rep (FullSubcategory c m o) x -> FullSubcategory c m o | |
(Show c, Show o) => Show (FullSubcategory c m o) Source # | |
Defined in Math.FiniteCategories.FullSubcategory showsPrec :: Int -> FullSubcategory c m o -> ShowS show :: FullSubcategory c m o -> String showList :: [FullSubcategory c m o] -> ShowS | |
(Eq c, Eq o) => Eq (FullSubcategory c m o) Source # | |
Defined in Math.FiniteCategories.FullSubcategory (==) :: FullSubcategory c m o -> FullSubcategory c m o -> Bool (/=) :: FullSubcategory c m o -> FullSubcategory c m o -> Bool | |
(Category c m o, Eq o) => Category (FullSubcategory c m o) m o Source # | |
Defined in Math.FiniteCategories.FullSubcategory identity :: FullSubcategory c m o -> o -> m Source # ar :: FullSubcategory c m o -> o -> o -> Set m Source # genAr :: FullSubcategory c m o -> o -> o -> Set m Source # decompose :: FullSubcategory c m o -> m -> [m] Source # | |
(Category c m o, Eq o) => FiniteCategory (FullSubcategory c m o) m o Source # | |
Defined in Math.FiniteCategories.FullSubcategory ob :: FullSubcategory c m o -> Set o Source # | |
type Rep (FullSubcategory c m o) Source # | |
Defined in Math.FiniteCategories.FullSubcategory type Rep (FullSubcategory c m o) = D1 ('MetaData "FullSubcategory" "Math.FiniteCategories.FullSubcategory" "FiniteCategories-0.6.3.1-inplace" 'False) (C1 ('MetaCons "FullSubcategory" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 c) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Set o)))) |
data InheritedFullSubcategory c m o Source #
An InheritedFullSubcategory
is a FullSubcategory
where the generators are the same as in the original Category
.
InheritedFullSubcategory c (Set o) |