oalg-base-3.0.0.0: Algebraic structures on oriented entities and limits as a tool kit to solve algebraic problems.
Copyright(c) Erich Gut
LicenseBSD3
Maintainerzerich.gut@gmail.com
Safe HaskellNone
LanguageHaskell2010

OAlg.Data.Ornt

Description

homomorphisms to Orientation.

Synopsis

Documentation

data Ornt s x y where Source #

homomorphisms to Orientation.

Constructors

Ornt :: forall s x. (Structure s x, Structure s (Orientation (Point x))) => Ornt s x (Orientation (Point x)) 
OrntMap :: forall s a b. (Structure s (Orientation a), Structure s (Orientation b)) => (a -> b) -> Ornt s (Orientation a) (Orientation b) 

Instances

Instances details
TransformableOrt s => ApplicativeG Id (Ornt s) (->) Source # 
Instance details

Defined in OAlg.Data.Ornt

Methods

amapG :: Ornt s x y -> Id x -> Id y Source #

Transformable s FbrOrt => ApplicativeG Rt (Ornt s) (->) Source # 
Instance details

Defined in OAlg.Data.Ornt

Methods

amapG :: Ornt s x y -> Rt x -> Rt y Source #

ApplicativeG Pnt (Ornt s) (->) Source # 
Instance details

Defined in OAlg.Data.Ornt

Methods

amapG :: Ornt s x y -> Pnt x -> Pnt y Source #

Morphism (Ornt s) Source # 
Instance details

Defined in OAlg.Data.Ornt

Associated Types

type ObjectClass (Ornt s) 
Instance details

Defined in OAlg.Data.Ornt

type ObjectClass (Ornt s) = s

Methods

homomorphous :: Ornt s x y -> Homomorphous (ObjectClass (Ornt s)) x y Source #

domain :: Ornt s x y -> Struct (ObjectClass (Ornt s)) x Source #

range :: Ornt s x y -> Struct (ObjectClass (Ornt s)) y Source #

TransformableTyp s => TransformableObjectClassTyp (Ornt s) Source # 
Instance details

Defined in OAlg.Data.Ornt

(TransformableFbrOrt s, TransformableAdd s) => HomAdditive (Ornt s) Source # 
Instance details

Defined in OAlg.Data.Ornt

TransformableDst s => HomDistributive (Ornt s) Source # 
Instance details

Defined in OAlg.Data.Ornt

TransformableFbrOrt s => HomFibred (Ornt s) Source # 
Instance details

Defined in OAlg.Data.Ornt

TransformableFbrOrt s => HomFibredOriented (Ornt s) Source # 
Instance details

Defined in OAlg.Data.Ornt

TransformableMlt s => HomMultiplicative (Ornt s) Source # 
Instance details

Defined in OAlg.Data.Ornt

TransformableOrt s => HomOriented (Ornt s) Source # 
Instance details

Defined in OAlg.Data.Ornt

type ObjectClass (Ornt s) Source # 
Instance details

Defined in OAlg.Data.Ornt

type ObjectClass (Ornt s) = s

orntAppl :: Transformable s Ort => Ornt s x y -> x -> y Source #

applying an Ornt.