| Copyright | Guillaume Sabbagh 2022 |
|---|---|
| License | GPL-3 |
| Maintainer | guillaumesabbagh@protonmail.com |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | Safe-Inferred |
| Language | Haskell2010 |
Math.FiniteCategories.FullSubcategory
Description
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.
Constructors
| FullSubcategory c (Set o) |
Instances
| (PrettyPrint c, PrettyPrint o, Eq o) => PrettyPrint (FullSubcategory c m o) Source # | |
Defined in Math.FiniteCategories.FullSubcategory Methods 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 Methods simplify :: FullSubcategory c m o -> FullSubcategory c m o # | |
| Generic (FullSubcategory c m o) Source # | |
Defined in Math.FiniteCategories.FullSubcategory Associated Types type Rep (FullSubcategory c m o) :: Type -> Type Methods 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 Methods 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 Methods (==) :: 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 Methods 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 Methods 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-0.6.4.0-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.
Constructors
| InheritedFullSubcategory c (Set o) |