Copyright	Guillaume Sabbagh 2022
License	GPL-3
Maintainer	guillaumesabbagh@protonmail.com
Stability	experimental
Portability	portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

Math.FiniteCategories.Ens.Examples

Description

Examples of Ens.

Synopsis

exampleEns :: Ens Char
exampleEns2 :: Ens Char
exampleDiscreteDiagToSet :: Diagram (DiscreteCategory Char) (DiscreteMorphism Char) Char (FinSet Int) (Function Int) (Set Int)
exampleProductSet :: Cone (DiscreteCategory Char) (DiscreteMorphism Char) Char (FinSet (Limit Char Int)) (Function (Limit Char Int)) (Set (Limit Char Int))
exampleCoproductSet :: Cocone (DiscreteCategory Char) (DiscreteMorphism Char) Char (FinSet (Colimit Char Int)) (Function (Colimit Char Int)) (Set (Colimit Char Int))
exampleParallelDiagramToSet :: Diagram Parallel ParallelAr ParallelOb (FinSet Int) (Function Int) (Set Int)
exampleEqualizerSet :: Cone Parallel ParallelAr ParallelOb (FinSet Int) (Function Int) (Set Int)
exampleCoequalizerSet :: Cocone Parallel ParallelAr ParallelOb (FinSet Int) (Function Int) (Set Int)
exampleDiagramVToFinSet :: Diagram V VAr VOb (FinSet Int) (Function Int) (Set Int)
exampleLimitSet :: Cone V VAr VOb (FinSet (Limit VOb Int)) (Function (Limit VOb Int)) (Set (Limit VOb Int))
exampleColimitSet :: Cocone Hat HatAr HatOb (FinSet (Colimit HatOb Int)) (Function (Colimit HatOb Int)) (Set (Colimit HatOb Int))
exampleExponentialObjectInSet :: Tripod (FinSet (Cartesian Int)) (Function (Cartesian Int)) (Set (Cartesian Int))

Documentation

exampleEns :: Ens Char Source #

An example of Ens containing all subsets of {A, B, C}.

exampleEns2 :: Ens Char Source #

An example of Ens containing sets {{},{A},{A,B},{A,B,C}}.

exampleDiscreteDiagToSet :: Diagram (DiscreteCategory Char) (DiscreteMorphism Char) Char (FinSet Int) (Function Int) (Set Int) Source #

An example of discreteDiagram to FinSet.

exampleProductSet :: Cone (DiscreteCategory Char) (DiscreteMorphism Char) Char (FinSet (Limit Char Int)) (Function (Limit Char Int)) (Set (Limit Char Int)) Source #

An example of product computed in FinSet thanks to the fact that FinSet is complete. Computes {1,2} x {3,4,5}.

exampleCoproductSet :: Cocone (DiscreteCategory Char) (DiscreteMorphism Char) Char (FinSet (Colimit Char Int)) (Function (Colimit Char Int)) (Set (Colimit Char Int)) Source #

An example of coproduct computed in FinSet thanks to the fact that FinSet is cocomplete. Computes {1,2} + {3,4,5}.

exampleParallelDiagramToSet :: Diagram Parallel ParallelAr ParallelOb (FinSet Int) (Function Int) (Set Int) Source #

An example of parallelDiagram to FinSet, the first function selected is x%2 on {0,1,2,3,4} and the second is (const 0).

exampleEqualizerSet :: Cone Parallel ParallelAr ParallelOb (FinSet Int) (Function Int) (Set Int) Source #

An example of equalizer of a parallelDiagram to FinSet thanks to the fact that FinSet is complete.

It equalizes exampleParallelDiagramToSet, therefore the apex of the equalizer is {0,2,4}.

exampleCoequalizerSet :: Cocone Parallel ParallelAr ParallelOb (FinSet Int) (Function Int) (Set Int) Source #

An example of coequalizer of a parallelDiagram to FinSet thanks to the fact that FinSet is cocomplete.

It equalizes exampleParallelDiagramToSet, therefore the nadir of the coequalizer is {0}.

exampleDiagramVToFinSet :: Diagram V VAr VOb (FinSet Int) (Function Int) (Set Int) Source #

An example of a diagram from V to FinSet. The two functions selected are identities, the first from {1,2,3,4} to {1,2,3,4,5,6,7,8,9,10} and the second from {3,4,5,6} to {1,2,3,4,5,6,7,8,9,10}.

exampleLimitSet :: Cone V VAr VOb (FinSet (Limit VOb Int)) (Function (Limit VOb Int)) (Set (Limit VOb Int)) Source #

An example of limit computation of a Diagram to FinSet thanks to the fact that FinSet is complete.

exampleColimitSet :: Cocone Hat HatAr HatOb (FinSet (Colimit HatOb Int)) (Function (Colimit HatOb Int)) (Set (Colimit HatOb Int)) Source #

An example of colimit computation of a Diagram to FinSet thanks to the fact that FinSet is cocomplete.

It is the colimit of exampleDiagramHatToFinSet which computes the union of {1,2,3,4} and {3,4,5,6} where 3 and 4 are identified.

exampleExponentialObjectInSet :: Tripod (FinSet (Cartesian Int)) (Function (Cartesian Int)) (Set (Cartesian Int)) Source #

An example of exponential object. Computes the internal hom of exampleDiscreteDiagToSet, meaning all functions from {1,2} to {3,4,5}.