module Math.Functors.KanExtension.Examples
(
exampleLeftKanExtension,
exampleRightKanExtension,
)
where
import Math.FiniteCategory
import Math.FiniteCategories
import Math.Functors.KanExtension
import Data.Text (Text)
import Data.WeakSet (Set)
import qualified Data.WeakSet as Set
import Data.WeakSet.Safe
import Data.WeakMap (Map)
import qualified Data.WeakMap as Map
import Data.WeakMap.Safe
exampleLeftKanExtension :: Diagram (CompositionGraph Text Text) (CGMorphism Text Text) Text (CompositionGraph Text Text) (CGMorphism Text Text) Text
exampleLeftKanExtension :: Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
exampleLeftKanExtension = Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
lk
where
a :: CompositionGraph Text Text
a = String -> CompositionGraph Text Text
unsafeReadCGString String
"A\nB\n"
b :: CompositionGraph Text Text
b = String -> CompositionGraph Text Text
unsafeReadCGString String
"A -q1-> C\nB -q2-> C\n"
c :: CompositionGraph Text Text
c = String -> CompositionGraph Text Text
unsafeReadCGString String
"0 -abs-> 1\n"
f :: Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
f = String
-> Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
unsafeReadCGDString String
"<SRC>\nA\nB\n</SRC>\n<TGT>\nA -q1-> C\nB -q2-> C\n</TGT>\nA => A\nB => B\n"
x :: Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
x = String
-> Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
unsafeReadCGDString String
"<SRC>\nA\nB\n</SRC>\n<TGT>\n0 -abs-> 1\n</TGT>\nA => 0\nB => 1"
Just (Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
lk,NaturalTransformation
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
lknat) = (Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
-> Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
-> Maybe
(Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text,
NaturalTransformation
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text)
forall c1 m1 o1 c2 m2 o2 c3 m3 o3.
(FiniteCategory c1 m1 o1, Morphism m1 o1, Eq c1, Eq m1, Eq o1,
FiniteCategory c2 m2 o2, Morphism m2 o2, Eq c2, Eq m2, Eq o2,
FiniteCategory c3 m3 o3, Morphism m3 o3, Eq c3, Eq m3, Eq o3) =>
Diagram c1 m1 o1 c2 m2 o2
-> Diagram c1 m1 o1 c3 m3 o3
-> Maybe
(Diagram c2 m2 o2 c3 m3 o3,
NaturalTransformation c1 m1 o1 c3 m3 o3)
leftKan Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
f Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
x)
exampleRightKanExtension :: Diagram (CompositionGraph Text Text) (CGMorphism Text Text) Text (CompositionGraph Text Text) (CGMorphism Text Text) Text
exampleRightKanExtension :: Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
exampleRightKanExtension = Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
rk
where
a :: CompositionGraph Text Text
a = String -> CompositionGraph Text Text
unsafeReadCGString String
"A\nB\n"
b :: CompositionGraph Text Text
b = String -> CompositionGraph Text Text
unsafeReadCGString String
"C -p1-> A\nC -p2-> B\n"
c :: CompositionGraph Text Text
c = String -> CompositionGraph Text Text
unsafeReadCGString String
"0 -abs-> 1\n"
f :: Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
f = String
-> Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
unsafeReadCGDString String
"<SRC>\nA\nB\n</SRC>\n<TGT>\nC -p1-> A\nC -p2-> B\n</TGT>\nA => A\nB => B\n"
x :: Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
x = String
-> Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
unsafeReadCGDString String
"<SRC>\nA\nB\n</SRC>\n<TGT>\n0 -abs-> 1\n</TGT>\nA => 0\nB => 1"
Just (Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
rk,NaturalTransformation
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
rknat) = (Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
-> Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
-> Maybe
(Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text,
NaturalTransformation
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text)
forall c1 m1 o1 c2 m2 o2 c3 m3 o3.
(FiniteCategory c1 m1 o1, Morphism m1 o1, Eq c1, Eq m1, Eq o1,
FiniteCategory c2 m2 o2, Morphism m2 o2, Eq c2, Eq m2, Eq o2,
FiniteCategory c3 m3 o3, Morphism m3 o3, Eq c3, Eq m3, Eq o3) =>
Diagram c1 m1 o1 c2 m2 o2
-> Diagram c1 m1 o1 c3 m3 o3
-> Maybe
(Diagram c2 m2 o2 c3 m3 o3,
NaturalTransformation c1 m1 o1 c3 m3 o3)
rightKan Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
f Diagram
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
(CompositionGraph Text Text)
(CGMorphism Text Text)
Text
x)