Copyright	(c) Erich Gut
License	BSD3
Maintainer	zerich.gut@gmail.com
Safe Haskell	Safe-Inferred
Language	Haskell2010

OAlg.Entity.Diagram.Quiver

Contents

Quiver
Duality

Description

the underlying Quiver of a Diagram.

Synopsis

data Quiver n m = Quiver (Any n) (FinList m (Orientation N))
qvOrientations :: Quiver n m -> FinList m (Orientation N)
coQuiver :: Quiver n m -> Dual (Quiver n m)
coQuiverInv :: Dual (Quiver n m) -> Quiver n m

Quiver

data Quiver n m Source #

quiver of n points and m arrows.

Property Let Quiver w o be in Quiver n m, then holds: For all 0 <= j < m holds: s j < n and e j < n where n = lengthN w, s j = start (o j) and e j = end (o j).

Constructors

Quiver (Any n) (FinList m (Orientation N))

Instances

Instances details

Show (Quiver n m) Source #
Instance details Defined in OAlg.Entity.Diagram.Quiver Methods showsPrec :: Int -> Quiver n m -> ShowS # show :: Quiver n m -> String # showList :: [Quiver n m] -> ShowS #
Eq (Quiver n m) Source #
Instance details Defined in OAlg.Entity.Diagram.Quiver Methods (==) :: Quiver n m -> Quiver n m -> Bool # (/=) :: Quiver n m -> Quiver n m -> Bool #
Validable (Quiver n m) Source #
Instance details Defined in OAlg.Entity.Diagram.Quiver Methods valid :: Quiver n m -> Statement Source #
(Typeable n, Typeable m) => Entity (Quiver n m) Source #
Instance details Defined in OAlg.Entity.Diagram.Quiver
type Dual (Quiver n m :: Type) Source #
Instance details Defined in OAlg.Entity.Diagram.Quiver type Dual (Quiver n m :: Type) = Quiver n m

qvOrientations :: Quiver n m -> FinList m (Orientation N) Source #

the orientation of the arrows of a quiver.

Duality

coQuiver :: Quiver n m -> Dual (Quiver n m) Source #

the dual of a quiver, with inverse coQuiverInv.

coQuiverInv :: Dual (Quiver n m) -> Quiver n m Source #

from the dual quiver, with inverse coQuiver.