OAlg.Category.Definition

categories of morphisms. We adapted the concept of categories form Category to better cover our needs.

Category

class Morphism c => Category c where

category of morphisms.

Properties Let c be a type instance of the class Category, then holds:

1. For all types x, y and f in c x y holds: cOne (range f) . f = f and f . cOne (domain f) = f.
2. For all types w, x, y, z and f in c x w, g in c y x, h in c z y holds: f . (g . h) = (f . g) . h.

Methods

cOne :: Struct (ObjectClass c) x -> c x x

the identity morphism for an eligible x.

(.) :: c y z -> c x y -> c x z infixr 9

Instances

Category (Homomorphous s)

Defined in OAlg.Category.Definition

Methods

cOne :: Struct (ObjectClass (Homomorphous s)) x -> Homomorphous s x x

(.) :: Homomorphous s y z -> Homomorphous s x y -> Homomorphous s x z

Morphism m => Category (Path m)

Defined in OAlg.Category.Path

Methods

cOne :: Struct (ObjectClass (Path m)) x -> Path m x x

(.) :: Path m y z -> Path m x y -> Path m x z

Category c => Category (Op2 c)

Defined in OAlg.Category.Definition

Methods

cOne :: Struct (ObjectClass (Op2 c)) x -> Op2 c x x

(.) :: Op2 c y z -> Op2 c x y -> Op2 c x z

Category (IdHom s)

Defined in OAlg.Hom.Oriented.Definition

Methods

cOne :: Struct (ObjectClass (IdHom s)) x -> IdHom s x x

(.) :: IdHom s y z -> IdHom s x y -> IdHom s x z

Category (IsoOp s)

Defined in OAlg.Hom.Oriented.Definition

Methods

cOne :: Struct (ObjectClass (IsoOp s)) x -> IsoOp s x x

(.) :: IsoOp s y z -> IsoOp s x y -> IsoOp s x z

Category (IsoOpMap f s)

Defined in OAlg.Hom.Oriented.Definition

Methods

cOne :: Struct (ObjectClass (IsoOpMap f s)) x -> IsoOpMap f s x x

(.) :: IsoOpMap f s y z -> IsoOpMap f s x y -> IsoOpMap f s x z

Category (->)

Defined in OAlg.Category.Definition

Methods

cOne :: Struct (ObjectClass (->)) x -> x -> x

(.) :: (y -> z) -> (x -> y) -> x -> z

cOne' :: Category c => p c -> Struct (ObjectClass c) x -> c x x

the cOne to a given Struct (ObjectClass c). The type p c serves only as proxy and cOne' is lazy in it.

Note As ObjectClass may be a non-injective type family, the type checker needs some times a little bit more information to pic the right cOne.

Some basic definitions in the category (->)

id :: x -> x

the identity map.

const :: b -> a -> b

the constant map given by a value in b.

Property Let y be in b then for all x in a holds: const y x is identical to y.

curry :: ((a, b) -> c) -> a -> b -> c

currying a map.

uncurry :: (a -> b -> c) -> (a, b) -> c

uncurrying a map.

fst :: (a, b) -> a

the first component of the pair.

snd :: (a, b) -> b

the second component of the pair.

curry3 :: ((a, b, c) -> d) -> a -> b -> c -> d

currying a map.

uncurry3 :: (a -> b -> c -> d) -> (a, b, c) -> d

uncurrying a map.

Cayleyan

class (Category c, Eq2 c) => Cayleyan2 c where

category of isomorphisms.

Property Let c be a type instance of Cayleyan2, then holds: For all types x, y and f in c x y holds: (invert2 f . f) == cOne (domain f) and (f . invert2 f) == cOne (range f) where (==) = eq2.

Methods

invert2 :: c x y -> c y x

Instances

Cayleyan2 (Homomorphous m)

Defined in OAlg.Category.Definition

Methods

invert2 :: Homomorphous m x y -> Homomorphous m y x

(Cayleyan2 m, EmbeddableMorphismTyp m) => Cayleyan2 (Path m)

Defined in OAlg.Category.Path

Methods

invert2 :: Path m x y -> Path m y x

Cayleyan2 c => Cayleyan2 (Op2 c)

Defined in OAlg.Category.Definition

Methods

invert2 :: Op2 c x y -> Op2 c y x

Cayleyan2 (IdHom s)

Defined in OAlg.Hom.Oriented.Definition

Methods

invert2 :: IdHom s x y -> IdHom s y x

ForgetfulTyp s => Cayleyan2 (IsoOp s)

Defined in OAlg.Hom.Oriented.Definition

Methods

invert2 :: IsoOp s x y -> IsoOp s y x

ForgetfulTyp s => Cayleyan2 (IsoOpMap f s)

Defined in OAlg.Hom.Oriented.Definition

Methods

invert2 :: IsoOpMap f s x y -> IsoOpMap f s y x

Morphism

class Morphism m where

morphism.

Minimal complete definition

homomorphous | domain, range

Associated Types

type ObjectClass m

the object class.

Methods

homomorphous :: m x y -> Homomorphous (ObjectClass m) x y

attests, that the types x and y fulfill the constraints given by Homomorphous (ObjectClass m) x y, i.e both fulfill the constraints given by Structure (ObjectClass m) x and Structure (ObjectClass m) y respectively.

domain :: m x y -> Struct (ObjectClass m) x

attests that the domain type x fulfills the constraints given by Structure (ObjectClass m) x.

range :: m x y -> Struct (ObjectClass m) y

attests that the range type y fulfills the constraints given by Structure (ObjectClass m) y.

Instances

Morphism GLApp

Defined in OAlg.Entity.Matrix.GeneralLinearGroup

Associated Types

type ObjectClass GLApp

Methods

homomorphous :: GLApp x y -> Homomorphous (ObjectClass GLApp) x y

domain :: GLApp x y -> Struct (ObjectClass GLApp) x

range :: GLApp x y -> Struct (ObjectClass GLApp) y

Morphism TrApp

Defined in OAlg.Entity.Matrix.GeneralLinearGroup

Associated Types

type ObjectClass TrApp

Methods

homomorphous :: TrApp x y -> Homomorphous (ObjectClass TrApp) x y

domain :: TrApp x y -> Struct (ObjectClass TrApp) x

range :: TrApp x y -> Struct (ObjectClass TrApp) y

Morphism (Homomorphous s)

Defined in OAlg.Category.Definition

Associated Types

type ObjectClass (Homomorphous s)

Methods

homomorphous :: Homomorphous s x y -> Homomorphous (ObjectClass (Homomorphous s)) x y

domain :: Homomorphous s x y -> Struct (ObjectClass (Homomorphous s)) x

range :: Homomorphous s x y -> Struct (ObjectClass (Homomorphous s)) y

Morphism m => Morphism (Path m)

Defined in OAlg.Category.Path

Associated Types

type ObjectClass (Path m)

Methods

homomorphous :: Path m x y -> Homomorphous (ObjectClass (Path m)) x y

domain :: Path m x y -> Struct (ObjectClass (Path m)) x

range :: Path m x y -> Struct (ObjectClass (Path m)) y

Morphism h => Morphism (Op2 h)

Defined in OAlg.Category.Definition

Associated Types

type ObjectClass (Op2 h)

Methods

homomorphous :: Op2 h x y -> Homomorphous (ObjectClass (Op2 h)) x y

domain :: Op2 h x y -> Struct (ObjectClass (Op2 h)) x

range :: Op2 h x y -> Struct (ObjectClass (Op2 h)) y

(Semiring r, Commutative r) => Morphism (HomSymbol r)

Defined in OAlg.Entity.Matrix.Vector

Associated Types

type ObjectClass (HomSymbol r)

Methods

homomorphous :: HomSymbol r x y -> Homomorphous (ObjectClass (HomSymbol r)) x y

domain :: HomSymbol r x y -> Struct (ObjectClass (HomSymbol r)) x

range :: HomSymbol r x y -> Struct (ObjectClass (HomSymbol r)) y

Morphism (SliceFactorDrop s)

Defined in OAlg.Entity.Slice.Definition

Associated Types

type ObjectClass (SliceFactorDrop s)

Methods

homomorphous :: SliceFactorDrop s x y -> Homomorphous (ObjectClass (SliceFactorDrop s)) x y

domain :: SliceFactorDrop s x y -> Struct (ObjectClass (SliceFactorDrop s)) x

range :: SliceFactorDrop s x y -> Struct (ObjectClass (SliceFactorDrop s)) y

Morphism (HomOp s)

Defined in OAlg.Hom.Oriented.Definition

Associated Types

type ObjectClass (HomOp s)

Methods

homomorphous :: HomOp s x y -> Homomorphous (ObjectClass (HomOp s)) x y

domain :: HomOp s x y -> Struct (ObjectClass (HomOp s)) x

range :: HomOp s x y -> Struct (ObjectClass (HomOp s)) y

Morphism (IdHom s)

Defined in OAlg.Hom.Oriented.Definition

Associated Types

type ObjectClass (IdHom s)

Methods

homomorphous :: IdHom s x y -> Homomorphous (ObjectClass (IdHom s)) x y

domain :: IdHom s x y -> Struct (ObjectClass (IdHom s)) x

range :: IdHom s x y -> Struct (ObjectClass (IdHom s)) y

Morphism (IsoOp s)

Defined in OAlg.Hom.Oriented.Definition

Associated Types

type ObjectClass (IsoOp s)

Methods

homomorphous :: IsoOp s x y -> Homomorphous (ObjectClass (IsoOp s)) x y

domain :: IsoOp s x y -> Struct (ObjectClass (IsoOp s)) x

range :: IsoOp s x y -> Struct (ObjectClass (IsoOp s)) y

Morphism h => Morphism (OpHom h)

Defined in OAlg.Hom.Oriented.Definition

Associated Types

type ObjectClass (OpHom h)

Methods

homomorphous :: OpHom h x y -> Homomorphous (ObjectClass (OpHom h)) x y

domain :: OpHom h x y -> Struct (ObjectClass (OpHom h)) x

range :: OpHom h x y -> Struct (ObjectClass (OpHom h)) y

Morphism m => Morphism (Forget t m)

Defined in OAlg.Category.Definition

Associated Types

type ObjectClass (Forget t m)

Methods

homomorphous :: Forget t m x y -> Homomorphous (ObjectClass (Forget t m)) x y

domain :: Forget t m x y -> Struct (ObjectClass (Forget t m)) x

range :: Forget t m x y -> Struct (ObjectClass (Forget t m)) y

(Morphism f, Morphism g, ObjectClass f ~ ObjectClass g) => Morphism (Either2 f g)

Defined in OAlg.Category.Definition

Associated Types

type ObjectClass (Either2 f g)

Methods

homomorphous :: Either2 f g x y -> Homomorphous (ObjectClass (Either2 f g)) x y

domain :: Either2 f g x y -> Struct (ObjectClass (Either2 f g)) x

range :: Either2 f g x y -> Struct (ObjectClass (Either2 f g)) y

(Multiplicative c, Sliced i c) => Morphism (SliceCokernelKernel i c)

Defined in OAlg.Entity.Slice.Adjunction

Associated Types

type ObjectClass (SliceCokernelKernel i c)

Methods

homomorphous :: SliceCokernelKernel i c x y -> Homomorphous (ObjectClass (SliceCokernelKernel i c)) x y

domain :: SliceCokernelKernel i c x y -> Struct (ObjectClass (SliceCokernelKernel i c)) x

range :: SliceCokernelKernel i c x y -> Struct (ObjectClass (SliceCokernelKernel i c)) y

Morphism (IsoOpMap f s)

Defined in OAlg.Hom.Oriented.Definition

Associated Types

type ObjectClass (IsoOpMap f s)

Methods

homomorphous :: IsoOpMap f s x y -> Homomorphous (ObjectClass (IsoOpMap f s)) x y

domain :: IsoOpMap f s x y -> Struct (ObjectClass (IsoOpMap f s)) x

range :: IsoOpMap f s x y -> Struct (ObjectClass (IsoOpMap f s)) y

Morphism (OpMap f s)

Defined in OAlg.Hom.Oriented.Definition

Associated Types

type ObjectClass (OpMap f s)

Methods

homomorphous :: OpMap f s x y -> Homomorphous (ObjectClass (OpMap f s)) x y

domain :: OpMap f s x y -> Struct (ObjectClass (OpMap f s)) x

range :: OpMap f s x y -> Struct (ObjectClass (OpMap f s)) y

Morphism (->)

Defined in OAlg.Category.Definition

Associated Types

type ObjectClass (->)

Methods

homomorphous :: (x -> y) -> Homomorphous (ObjectClass (->)) x y

domain :: (x -> y) -> Struct (ObjectClass (->)) x

range :: (x -> y) -> Struct (ObjectClass (->)) y

data Homomorphous s x y

attest that both x and y have homomorphous structures, i.e. both admit the same constraints given by the parameter s.

Constructors

(Struct s x) :>: (Struct s y) infix 5

Instances

Category (Homomorphous s)

Defined in OAlg.Category.Definition

Methods

cOne :: Struct (ObjectClass (Homomorphous s)) x -> Homomorphous s x x

(.) :: Homomorphous s y z -> Homomorphous s x y -> Homomorphous s x z

Cayleyan2 (Homomorphous m)

Defined in OAlg.Category.Definition

Methods

invert2 :: Homomorphous m x y -> Homomorphous m y x

Morphism (Homomorphous s)

Defined in OAlg.Category.Definition

Associated Types

type ObjectClass (Homomorphous s)

Methods

homomorphous :: Homomorphous s x y -> Homomorphous (ObjectClass (Homomorphous s)) x y

domain :: Homomorphous s x y -> Struct (ObjectClass (Homomorphous s)) x

range :: Homomorphous s x y -> Struct (ObjectClass (Homomorphous s)) y

Eq2 (Homomorphous m)

Defined in OAlg.Category.Definition

Methods

eq2 :: Homomorphous m x y -> Homomorphous m x y -> Bool

Show2 (Homomorphous m)

Defined in OAlg.Category.Definition

Methods

show2 :: Homomorphous m a b -> String

Show (Homomorphous s x y)

Defined in OAlg.Category.Definition

Methods

showsPrec :: Int -> Homomorphous s x y -> ShowS

show :: Homomorphous s x y -> String

showList :: [Homomorphous s x y] -> ShowS

Eq (Homomorphous s x y)

Defined in OAlg.Category.Definition

Methods

(==) :: Homomorphous s x y -> Homomorphous s x y -> Bool

(/=) :: Homomorphous s x y -> Homomorphous s x y -> Bool

type ObjectClass (Homomorphous s)

Defined in OAlg.Category.Definition

type ObjectClass (Homomorphous s) = s

tauHom :: Transformable s t => Homomorphous s x y -> Homomorphous t x y

transforming homomorphous structural attests.

tau1Hom :: Transformable1 f s => Homomorphous s x y -> Homomorphous s (f x) (f y)

transforming homomorphous structural attests.

eqlDomain :: Struct Typ x -> Struct Typ x' -> m x y -> m x' y -> Maybe (x :~: x')

gets for two Typeable types x and x' and for two parameterized types maybe an attest that the domain types are equal.

eqlRange :: Struct Typ y -> Struct Typ y' -> m x y -> m x y' -> Maybe (y :~: y')

gets for two Typeable types y and y' and for two parameterized types maybe an attest that the range types are equal.

eqlMorphism :: Typeable m => Struct Typ x -> Struct Typ x' -> Struct Typ y -> Struct Typ y' -> m x y -> m x' y' -> Maybe (m x y :~: m x' y')

gets maybe an attest that the two given morphisms types are equal.

Applicative

class Applicative h where

family of types having a representation in (->).

Methods

amap :: h a b -> a -> b

application.

Instances

Applicative GLApp

Defined in OAlg.Entity.Matrix.GeneralLinearGroup

Methods

amap :: GLApp a b -> a -> b

Applicative TrApp

Defined in OAlg.Entity.Matrix.GeneralLinearGroup

Methods

amap :: TrApp a b -> a -> b

Applicative m => Applicative (Path m)

Defined in OAlg.Category.Path

Methods

amap :: Path m a b -> a -> b

(Semiring r, Commutative r) => Applicative (HomSymbol r)

Defined in OAlg.Entity.Matrix.Vector

Methods

amap :: HomSymbol r a b -> a -> b

Applicative (SliceFactorDrop s)

Defined in OAlg.Entity.Slice.Definition

Methods

amap :: SliceFactorDrop s a b -> a -> b

ForgetfulOrt s => Applicative (HomOp s)

Defined in OAlg.Hom.Oriented.Definition

Methods

amap :: HomOp s a b -> a -> b

Applicative (IdHom s)

Defined in OAlg.Hom.Oriented.Definition

Methods

amap :: IdHom s a b -> a -> b

ForgetfulOrt s => Applicative (IsoOp s)

Defined in OAlg.Hom.Oriented.Definition

Methods

amap :: IsoOp s a b -> a -> b

Applicative h => Applicative (OpHom h)

Defined in OAlg.Hom.Oriented.Definition

Methods

amap :: OpHom h a b -> a -> b

Applicative m => Applicative (Forget t m)

Defined in OAlg.Category.Definition

Methods

amap :: Forget t m a b -> a -> b

(Applicative f, Applicative g) => Applicative (Either2 f g)

Defined in OAlg.Category.Applicative

Methods

amap :: Either2 f g a b -> a -> b

(Distributive c, SliceCokernelTo i c, SliceKernelFrom i c) => Applicative (SliceCokernelKernel i c)

Defined in OAlg.Entity.Slice.Adjunction

Methods

amap :: SliceCokernelKernel i c a b -> a -> b

ForgetfulDst s => Applicative (IsoOpMap Matrix s)

Defined in OAlg.Entity.Matrix.Definition

Methods

amap :: IsoOpMap Matrix s a b -> a -> b

ForgetfulOrt s => Applicative (IsoOpMap Path s)

Defined in OAlg.Hom.Oriented.Definition

Methods

amap :: IsoOpMap Path s a b -> a -> b

ForgetfulDst s => Applicative (OpMap Matrix s)

Defined in OAlg.Entity.Matrix.Definition

Methods

amap :: OpMap Matrix s a b -> a -> b

ForgetfulOrt s => Applicative (OpMap Path s)

Defined in OAlg.Hom.Oriented.Definition

Methods

amap :: OpMap Path s a b -> a -> b

Applicative (->)

Defined in OAlg.Category.Applicative

Methods

amap :: (a -> b) -> a -> b

($) :: Applicative h => h a b -> a -> b infixr 0

right associative application on values.

class Applicative1 h f where

family of types having a representation in f a -> f b.

Methods

amap1 :: h a b -> f a -> f b

application.

Instances

HomDistributive h => Applicative1 h Matrix

Defined in OAlg.Entity.Matrix.Definition

Methods

amap1 :: h a b -> Matrix a -> Matrix b

HomOriented h => Applicative1 h (Diagram t n m)

Defined in OAlg.Entity.Diagram.Definition

Methods

amap1 :: h a b -> Diagram t n m a -> Diagram t n m b

HomDistributive h => Applicative1 h (Cone Dst p t n m)

Defined in OAlg.Limes.Cone.Definition

Methods

amap1 :: h a b -> Cone Dst p t n m a -> Cone Dst p t n m b

HomMultiplicative h => Applicative1 h (Cone Mlt p t n m)

Defined in OAlg.Limes.Cone.Definition

Methods

amap1 :: h a b -> Cone Mlt p t n m a -> Cone Mlt p t n m b

IsoMultiplicative h => Applicative1 h (Limes Mlt p t n m)

Defined in OAlg.Limes.Definition

Methods

amap1 :: h a b -> Limes Mlt p t n m a -> Limes Mlt p t n m b

IsoDistributive h => Applicative1 h (Limits Dst p t n m)

Defined in OAlg.Limes.Limits

Methods

amap1 :: h a b -> Limits Dst p t n m a -> Limits Dst p t n m b

IsoMultiplicative h => Applicative1 h (Limits Mlt p t n m)

Defined in OAlg.Limes.Limits

Methods

amap1 :: h a b -> Limits Mlt p t n m a -> Limits Mlt p t n m b

Functor f => Applicative1 (->) f

Defined in OAlg.Category.Applicative

Methods

amap1 :: (a -> b) -> f a -> f b

Functorial

class (Applicative c, Category c) => Functorial c

representable categories, i.e. covariant functors from an Applicative category c to (->).

Properties Let c be a type instance of the class Functorial then holds:

1. For all types x and d in Struct (ObjectClass c) x holds: amap (cOne d) = id.
2. For all types x, y, z and f in c y z, g in c x y holds: amap (f . g) = amap f . amap g.

Instances

(Applicative m, Morphism m) => Functorial (Path m)

Defined in OAlg.Category.Path

Functorial (IdHom s)

Defined in OAlg.Hom.Oriented.Definition

ForgetfulOrt s => Functorial (IsoOp s)

Defined in OAlg.Hom.Oriented.Definition

ForgetfulDst s => Functorial (IsoOpMap Matrix s)

Defined in OAlg.Entity.Matrix.Definition

ForgetfulOrt s => Functorial (IsoOpMap Path s)

Defined in OAlg.Hom.Oriented.Definition

Forget

data Forget t m x y where

forgets the ObjectClass of m and sets it to t, under the condition that the ObjectClass of m is Transformable to t.

Constructors

Forget :: Transformable (ObjectClass m) t => m x y -> Forget t m x y

Instances

Applicative m => Applicative (Forget t m)

Defined in OAlg.Category.Definition

Methods

amap :: Forget t m a b -> a -> b

(Morphism m, ForgetfulTyp t) => EmbeddableMorphismTyp (Forget t m)

Defined in OAlg.Category.Definition

Morphism m => Morphism (Forget t m)

Defined in OAlg.Category.Definition

Associated Types

type ObjectClass (Forget t m)

Methods

homomorphous :: Forget t m x y -> Homomorphous (ObjectClass (Forget t m)) x y

domain :: Forget t m x y -> Struct (ObjectClass (Forget t m)) x

range :: Forget t m x y -> Struct (ObjectClass (Forget t m)) y

Eq2 m => Eq2 (Forget t m)

Defined in OAlg.Category.Definition

Methods

eq2 :: Forget t m x y -> Forget t m x y -> Bool

Show2 m => Show2 (Forget t m)

Defined in OAlg.Category.Definition

Methods

show2 :: Forget t m a b -> String

Validable2 m => Validable2 (Forget t m)

Defined in OAlg.Data.Validable

Methods

valid2 :: Forget t m x y -> Statement

(Entity2 h, Typeable t) => Entity2 (Forget t h)

Defined in OAlg.Entity.Definition

(HomMultiplicative h, Transformable1 Op t, ForgetfulMlt t, ForgetfulTyp t, Typeable t) => HomMultiplicative (Forget t h)

Defined in OAlg.Hom.Multiplicative.Definition

(HomOriented h, Transformable1 Op t, ForgetfulOrt t, ForgetfulTyp t, Typeable t) => HomOriented (Forget t h)

Defined in OAlg.Hom.Oriented.Definition

Methods

pmap :: Forget t h a b -> Point a -> Point b

(Morphism m, Transformable s t) => EmbeddableMorphism (Forget s m) t

Defined in OAlg.Category.Definition

Show2 m => Show (Forget t m x y)

Defined in OAlg.Category.Definition

Methods

showsPrec :: Int -> Forget t m x y -> ShowS

show :: Forget t m x y -> String

showList :: [Forget t m x y] -> ShowS

Eq2 m => Eq (Forget t m x y)

Defined in OAlg.Category.Definition

Methods

(==) :: Forget t m x y -> Forget t m x y -> Bool

(/=) :: Forget t m x y -> Forget t m x y -> Bool

Validable2 m => Validable (Forget t m x y)

Defined in OAlg.Data.Validable

Methods

valid :: Forget t m x y -> Statement

type ObjectClass (Forget t m)

Defined in OAlg.Category.Definition

type ObjectClass (Forget t m) = t

Embeddable

class (Morphism m, Transformable (ObjectClass m) t) => EmbeddableMorphism m t

morphism for which its object class can be embedded into the given structure.

Instances

EmbeddableMorphism GLApp Typ

Defined in OAlg.Entity.Matrix.GeneralLinearGroup

EmbeddableMorphism GLApp Mlt

Defined in OAlg.Entity.Matrix.GeneralLinearGroup

EmbeddableMorphism GLApp Ort

Defined in OAlg.Entity.Matrix.GeneralLinearGroup

EmbeddableMorphism TrApp Typ

Defined in OAlg.Entity.Matrix.GeneralLinearGroup

EmbeddableMorphism TrApp Ort

Defined in OAlg.Entity.Matrix.GeneralLinearGroup

EmbeddableMorphism m t => EmbeddableMorphism (Path m) t

Defined in OAlg.Category.Path

EmbeddableMorphism m t => EmbeddableMorphism (Op2 m) t

Defined in OAlg.Category.Definition

(Semiring r, Commutative r) => EmbeddableMorphism (HomSymbol r) Add

Defined in OAlg.Entity.Matrix.Vector

(Semiring r, Commutative r) => EmbeddableMorphism (HomSymbol r) Typ

Defined in OAlg.Entity.Matrix.Vector

(Semiring r, Commutative r) => EmbeddableMorphism (HomSymbol r) Fbr

Defined in OAlg.Entity.Matrix.Vector

EmbeddableMorphism (SliceFactorDrop s) Typ

Defined in OAlg.Entity.Slice.Definition

EmbeddableMorphism (SliceFactorDrop s) Mlt

Defined in OAlg.Entity.Slice.Definition

EmbeddableMorphism (SliceFactorDrop s) Ort

Defined in OAlg.Entity.Slice.Definition

Transformable s t => EmbeddableMorphism (HomOp s) t

Defined in OAlg.Hom.Oriented.Definition

Transformable s t => EmbeddableMorphism (IdHom s) t

Defined in OAlg.Hom.Oriented.Definition

Transformable s t => EmbeddableMorphism (IsoOp s) t

Defined in OAlg.Hom.Oriented.Definition

EmbeddableMorphism h Add => EmbeddableMorphism (OpHom h) Add

Defined in OAlg.Hom.Oriented.Definition

EmbeddableMorphism h Typ => EmbeddableMorphism (OpHom h) Typ

Defined in OAlg.Hom.Oriented.Definition

EmbeddableMorphism h Dst => EmbeddableMorphism (OpHom h) Dst

Defined in OAlg.Hom.Oriented.Definition

EmbeddableMorphism h Fbr => EmbeddableMorphism (OpHom h) Fbr

Defined in OAlg.Hom.Oriented.Definition

EmbeddableMorphism h FbrOrt => EmbeddableMorphism (OpHom h) FbrOrt

Defined in OAlg.Hom.Oriented.Definition

EmbeddableMorphism h Mlt => EmbeddableMorphism (OpHom h) Mlt

Defined in OAlg.Hom.Oriented.Definition

EmbeddableMorphism h Ort => EmbeddableMorphism (OpHom h) Ort

Defined in OAlg.Hom.Oriented.Definition

(Semiring r, Commutative r) => EmbeddableMorphism (HomSymbol r) (Vec r)

Defined in OAlg.Entity.Matrix.Vector

(Morphism m, Transformable s t) => EmbeddableMorphism (Forget s m) t

Defined in OAlg.Category.Definition

(Multiplicative c, Sliced i c) => EmbeddableMorphism (SliceCokernelKernel i c) Typ

Defined in OAlg.Entity.Slice.Adjunction

(Multiplicative c, Sliced i c) => EmbeddableMorphism (SliceCokernelKernel i c) Mlt

Defined in OAlg.Entity.Slice.Adjunction

(Multiplicative c, Sliced i c) => EmbeddableMorphism (SliceCokernelKernel i c) Ort

Defined in OAlg.Entity.Slice.Adjunction

Transformable s t => EmbeddableMorphism (IsoOpMap f s) t

Defined in OAlg.Hom.Oriented.Definition

Transformable s t => EmbeddableMorphism (OpMap f s) t

Defined in OAlg.Hom.Oriented.Definition

class EmbeddableMorphism m Typ => EmbeddableMorphismTyp m

helper class to avoid undecidable instances.

Instances

EmbeddableMorphismTyp GLApp

Defined in OAlg.Entity.Matrix.GeneralLinearGroup

EmbeddableMorphismTyp TrApp

Defined in OAlg.Entity.Matrix.GeneralLinearGroup

EmbeddableMorphismTyp m => EmbeddableMorphismTyp (Path m)

Defined in OAlg.Category.Path

EmbeddableMorphismTyp m => EmbeddableMorphismTyp (Op2 m)

Defined in OAlg.Category.Definition

(Semiring r, Commutative r) => EmbeddableMorphismTyp (HomSymbol r)

Defined in OAlg.Entity.Matrix.Vector

EmbeddableMorphismTyp (SliceFactorDrop s)

Defined in OAlg.Entity.Slice.Definition

ForgetfulTyp s => EmbeddableMorphismTyp (HomOp s)

Defined in OAlg.Hom.Oriented.Definition

ForgetfulTyp s => EmbeddableMorphismTyp (IdHom s)

Defined in OAlg.Hom.Oriented.Definition

ForgetfulTyp s => EmbeddableMorphismTyp (IsoOp s)

Defined in OAlg.Hom.Oriented.Definition

EmbeddableMorphismTyp h => EmbeddableMorphismTyp (OpHom h)

Defined in OAlg.Hom.Oriented.Definition

(Morphism m, ForgetfulTyp t) => EmbeddableMorphismTyp (Forget t m)

Defined in OAlg.Category.Definition

(Multiplicative c, Sliced i c) => EmbeddableMorphismTyp (SliceCokernelKernel i c)

Defined in OAlg.Entity.Slice.Adjunction

ForgetfulTyp s => EmbeddableMorphismTyp (IsoOpMap f s)

Defined in OAlg.Hom.Oriented.Definition

ForgetfulTyp s => EmbeddableMorphismTyp (OpMap f s)

Defined in OAlg.Hom.Oriented.Definition