Copyright	Guillaume Sabbagh 2022
License	GPL-3
Maintainer	guillaumesabbagh@protonmail.com
Stability	experimental
Portability	portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

Math.FiniteCategories.LimitCategory

Contents

Limit category
Orphan instances

Description

A LimitCategory is the category in which the limit of a diagram in FinCat lives. To compute limits in a usual category, see Math.CompleteCategory. To compute limits in a custom FiniteCategory, see limits in Math.ConeCategory.

Synopsis

data LimitCategory cIndex mIndex oIndex c m o
- = ProjectedCategory c
- | LimitCategory (Diagram cIndex mIndex oIndex (FinCat c m o) (FinFunctor c m o) c)

Limit category

data LimitCategory cIndex mIndex oIndex c m o Source #

A LimitCategory is either a ProjectedCategory (an original category) or a LimitCategory.

Constructors

ProjectedCategory c	An original category in `FinCat` with the indexing object of the category.
LimitCategory (Diagram cIndex mIndex oIndex (FinCat c m o) (FinFunctor c m o) c)	The limit category of a given `Diagram`.

Instances

Instances details

(FiniteCategory c m o, Morphism m o, Eq c, Eq m, Eq o, FiniteCategory cIndex mIndex oIndex, Morphism mIndex oIndex, Eq cIndex, Eq mIndex, Eq oIndex) => CompleteCategory (FinCat c m o) (FinFunctor c m o) c (FinCat (LimitCategory cIndex mIndex oIndex c m o) (Limit oIndex m) (Limit oIndex o)) (FinFunctor (LimitCategory cIndex mIndex oIndex c m o) (Limit oIndex m) (Limit oIndex o)) (LimitCategory cIndex mIndex oIndex c m o) cIndex mIndex oIndex Source #
Instance details Defined in Math.FiniteCategories.LimitCategory Methods limit :: Diagram cIndex mIndex oIndex (FinCat c m o) (FinFunctor c m o) c -> Cone cIndex mIndex oIndex (FinCat (LimitCategory cIndex mIndex oIndex c m o) (Limit oIndex m) (Limit oIndex o)) (FinFunctor (LimitCategory cIndex mIndex oIndex c m o) (Limit oIndex m) (Limit oIndex o)) (LimitCategory cIndex mIndex oIndex c m o) Source # projectBase :: Diagram cIndex mIndex oIndex (FinCat c m o) (FinFunctor c m o) c -> Diagram (FinCat c m o) (FinFunctor c m o) c (FinCat (LimitCategory cIndex mIndex oIndex c m o) (Limit oIndex m) (Limit oIndex o)) (FinFunctor (LimitCategory cIndex mIndex oIndex c m o) (Limit oIndex m) (Limit oIndex o)) (LimitCategory cIndex mIndex oIndex c m o) Source #
(PrettyPrint c, PrettyPrint cIndex, PrettyPrint oIndex, PrettyPrint mIndex, PrettyPrint o, PrettyPrint m, Eq o, Eq m, Eq oIndex, Eq c, Eq mIndex, FiniteCategory c m o, Morphism m o) => PrettyPrint (LimitCategory cIndex mIndex oIndex c m o) Source #
Instance details Defined in Math.FiniteCategories.LimitCategory Methods pprint :: Int -> LimitCategory cIndex mIndex oIndex c m o -> String Source # pprintWithIndentations :: Int -> Int -> String -> LimitCategory cIndex mIndex oIndex c m o -> String Source # pprintIndent :: Int -> LimitCategory cIndex mIndex oIndex c m o -> String Source #
(Simplifiable c, Simplifiable cIndex, Simplifiable oIndex, Simplifiable mIndex, Simplifiable o, Simplifiable m, Eq o, Eq m, Eq oIndex, Eq mIndex) => Simplifiable (LimitCategory cIndex mIndex oIndex c m o) Source #
Instance details Defined in Math.FiniteCategories.LimitCategory Methods simplify :: LimitCategory cIndex mIndex oIndex c m o -> LimitCategory cIndex mIndex oIndex c m o #
Generic (LimitCategory cIndex mIndex oIndex c m o) Source #
Instance details Defined in Math.FiniteCategories.LimitCategory Associated Types type Rep (LimitCategory cIndex mIndex oIndex c m o) :: Type -> Type Methods from :: LimitCategory cIndex mIndex oIndex c m o -> Rep (LimitCategory cIndex mIndex oIndex c m o) x to :: Rep (LimitCategory cIndex mIndex oIndex c m o) x -> LimitCategory cIndex mIndex oIndex c m o
(Show c, Show cIndex, Show oIndex, Show mIndex, Show o, Show m) => Show (LimitCategory cIndex mIndex oIndex c m o) Source #
Instance details Defined in Math.FiniteCategories.LimitCategory Methods showsPrec :: Int -> LimitCategory cIndex mIndex oIndex c m o -> ShowS show :: LimitCategory cIndex mIndex oIndex c m o -> String showList :: [LimitCategory cIndex mIndex oIndex c m o] -> ShowS
(Eq c, Eq cIndex, Eq mIndex, Eq oIndex, Eq m, Eq o, FiniteCategory c m o, FiniteCategory cIndex mIndex oIndex, Morphism m o, Morphism mIndex oIndex) => Eq (LimitCategory cIndex mIndex oIndex c m o) Source #
Instance details Defined in Math.FiniteCategories.LimitCategory Methods (==) :: LimitCategory cIndex mIndex oIndex c m o -> LimitCategory cIndex mIndex oIndex c m o -> Bool (/=) :: LimitCategory cIndex mIndex oIndex c m o -> LimitCategory cIndex mIndex oIndex c m o -> Bool
(FiniteCategory cIndex mIndex oIndex, Morphism mIndex oIndex, Eq mIndex, Eq oIndex, Category c m o, Morphism m o, Eq m, Eq o) => Category (LimitCategory cIndex mIndex oIndex c m o) (Limit oIndex m) (Limit oIndex o) Source #
Instance details Defined in Math.FiniteCategories.LimitCategory Methods identity :: LimitCategory cIndex mIndex oIndex c m o -> Limit oIndex o -> Limit oIndex m Source # ar :: LimitCategory cIndex mIndex oIndex c m o -> Limit oIndex o -> Limit oIndex o -> Set (Limit oIndex m) Source # genAr :: LimitCategory cIndex mIndex oIndex c m o -> Limit oIndex o -> Limit oIndex o -> Set (Limit oIndex m) Source # decompose :: LimitCategory cIndex mIndex oIndex c m o -> Limit oIndex m -> [Limit oIndex m] Source #
(FiniteCategory cIndex mIndex oIndex, Morphism mIndex oIndex, Eq mIndex, Eq oIndex, FiniteCategory c m o, Morphism m o, Eq m, Eq o) => FiniteCategory (LimitCategory cIndex mIndex oIndex c m o) (Limit oIndex m) (Limit oIndex o) Source #
Instance details Defined in Math.FiniteCategories.LimitCategory Methods ob :: LimitCategory cIndex mIndex oIndex c m o -> Set (Limit oIndex o) Source #
type Rep (LimitCategory cIndex mIndex oIndex c m o) Source #
Instance details Defined in Math.FiniteCategories.LimitCategory type Rep (LimitCategory cIndex mIndex oIndex c m o) = D1 ('MetaData "LimitCategory" "Math.FiniteCategories.LimitCategory" "FiniteCategories-0.6.4.0-inplace" 'False) (C1 ('MetaCons "ProjectedCategory" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 c)) :+: C1 ('MetaCons "LimitCategory" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Diagram cIndex mIndex oIndex (FinCat c m o) (FinFunctor c m o) c))))

Orphan instances

(Morphism m o, Eq m, Eq oIndex) => Morphism (Limit oIndex m) (Limit oIndex o) Source #
Instance details Methods (@) :: Limit oIndex m -> Limit oIndex m -> Limit oIndex m Source # (@?) :: Limit oIndex m -> Limit oIndex m -> Maybe (Limit oIndex m) Source # source :: Limit oIndex m -> Limit oIndex o Source # target :: Limit oIndex m -> Limit oIndex o Source #