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

OAlg.Hom.Fibred

Contents

Fibred
Fibred Oriented
Proposition

Description

homomorphisms between Fibred structures

Synopsis

class (EmbeddableMorphism h Fbr, Applicative h, Entity2 h, EmbeddableMorphismTyp h) => HomFibred h where
- rmap :: h a b -> Root a -> Root b
class (Category h, Functorial h, HomFibred h) => FunctorialHomFibred h
class (EmbeddableMorphism h FbrOrt, HomFibred h, HomOriented h) => HomFibredOriented h
prpHomFbrOrt :: HomFibredOriented h => h a b -> Root a -> Statement

Fibred

class (EmbeddableMorphism h Fbr, Applicative h, Entity2 h, EmbeddableMorphismTyp h) => HomFibred h where Source #

type family of homomorphisms between Fibred structures.

Property Let h be an instance of HomFibred then for all a, b and f in h a b and x in a holds: root (amap f x) == rmap f (root x).

Minimal complete definition

Nothing

Methods

rmap :: h a b -> Root a -> Root b Source #

default rmap :: (EmbeddableMorphism h FbrOrt, HomOriented h) => h a b -> Root a -> Root b Source #

Instances

Instances details

HomFibred h => HomFibred (Path h) Source #
Instance details Defined in OAlg.Hom.Fibred Methods rmap :: Path h a b -> Root a -> Root b Source #
(Semiring r, Commutative r) => HomFibred (HomSymbol r) Source #
Instance details Defined in OAlg.Entity.Matrix.Vector Methods rmap :: HomSymbol r a b -> Root a -> Root b Source #
(TransformableOp s, ForgetfulFbrOrt s, ForgetfulTyp s, Typeable s) => HomFibred (HomOp s) Source #
Instance details Defined in OAlg.Hom.Fibred Methods rmap :: HomOp s a b -> Root a -> Root b Source #
(ForgetfulFbr s, ForgetfulTyp s, Typeable s) => HomFibred (IdHom s) Source #
Instance details Defined in OAlg.Hom.Fibred Methods rmap :: IdHom s a b -> Root a -> Root b Source #
(TransformableOp s, ForgetfulFbrOrt s, ForgetfulTyp s, Typeable s) => HomFibred (IsoOp s) Source #
Instance details Defined in OAlg.Hom.Fibred Methods rmap :: IsoOp s a b -> Root a -> Root b Source #
HomFibredOriented h => HomFibred (OpHom h) Source #
Instance details Defined in OAlg.Hom.Fibred Methods rmap :: OpHom h a b -> Root a -> Root b Source #
(TransformableOp s, ForgetfulDst s, ForgetfulTyp s, Typeable s) => HomFibred (IsoOpMap Matrix s) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition Methods rmap :: IsoOpMap Matrix s a b -> Root a -> Root b Source #
(TransformableOp s, ForgetfulDst s, ForgetfulTyp s, Typeable s) => HomFibred (OpMap Matrix s) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition Methods rmap :: OpMap Matrix s a b -> Root a -> Root b Source #

class (Category h, Functorial h, HomFibred h) => FunctorialHomFibred h Source #

functorial application of Fibred homomorphisms.

Instances

Instances details

FunctorialHomFibred h => FunctorialHomFibred (Path h) Source #
Instance details Defined in OAlg.Hom.Fibred

Fibred Oriented

class (EmbeddableMorphism h FbrOrt, HomFibred h, HomOriented h) => HomFibredOriented h Source #

type family of homomorphisms between FibredOriented structures.

Property Let h be an instance of HomFibredOriented then for all a, b and f in h a b and r in Root a holds: rmap f r == omap f r.

Instances

Instances details

HomFibredOriented h => HomFibredOriented (Path h) Source #
Instance details Defined in OAlg.Hom.Fibred
(TransformableOp s, ForgetfulFbrOrt s, ForgetfulTyp s, Typeable s) => HomFibredOriented (HomOp s) Source #
Instance details Defined in OAlg.Hom.Fibred
(TransformableOp s, ForgetfulFbrOrt s, ForgetfulTyp s, Typeable s) => HomFibredOriented (IdHom s) Source #
Instance details Defined in OAlg.Hom.Fibred
(TransformableOp s, ForgetfulFbrOrt s, ForgetfulTyp s, Typeable s) => HomFibredOriented (IsoOp s) Source #
Instance details Defined in OAlg.Hom.Fibred
HomFibredOriented h => HomFibredOriented (OpHom h) Source #
Instance details Defined in OAlg.Hom.Fibred
(TransformableOp s, ForgetfulDst s, ForgetfulTyp s, Typeable s) => HomFibredOriented (IsoOpMap Matrix s) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition
(TransformableOp s, ForgetfulDst s, ForgetfulTyp s, Typeable s) => HomFibredOriented (OpMap Matrix s) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition

Proposition

prpHomFbrOrt :: HomFibredOriented h => h a b -> Root a -> Statement Source #

validity according to HomFibredOriented.