Math.FiniteCategories.Ens.Examples

Examples of Ens.

Documentation

exampleEns :: Ens Char

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

exampleEns2 :: Ens Char

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)

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))

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))

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)

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)

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)

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)

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))

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))

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))

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