| Copyright | Guillaume Sabbagh 2023 |
|---|---|
| License | GPL-3 |
| Maintainer | guillaumesabbagh@protonmail.com |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | Safe-Inferred |
| Language | Haskell2010 |
Math.Functors.SetValued.Examples
Description
Examples of Kan extensions of set-valued functors.
Kan extensions of set-valued functors are useful for the study of models of linear sketches.
Synopsis
- exampleSetValuedLeftKanExtension :: (Diagram (CompositionGraph Text Text) (CGMorphism Text Text) Text (FinSet (ColimitObject Text (CGMorphism Text Text) Int)) (Function (ColimitObject Text (CGMorphism Text Text) Int)) (Set (ColimitObject Text (CGMorphism Text Text) Int)), NaturalTransformation (CompositionGraph Text Text) (CGMorphism Text Text) Text (FinSet (ColimitObject Text (CGMorphism Text Text) Int)) (Function (ColimitObject Text (CGMorphism Text Text) Int)) (Set (ColimitObject Text (CGMorphism Text Text) Int)))
- exampleSetValuedRightKanExtension :: (Diagram (CompositionGraph Text Text) (CGMorphism Text Text) Text (FinSet (LimitObject Text (CGMorphism Text Text) Int)) (Function (LimitObject Text (CGMorphism Text Text) Int)) (Set (LimitObject Text (CGMorphism Text Text) Int)), NaturalTransformation (CompositionGraph Text Text) (CGMorphism Text Text) Text (FinSet (LimitObject Text (CGMorphism Text Text) Int)) (Function (LimitObject Text (CGMorphism Text Text) Int)) (Set (LimitObject Text (CGMorphism Text Text) Int)))
Documentation
exampleSetValuedLeftKanExtension :: (Diagram (CompositionGraph Text Text) (CGMorphism Text Text) Text (FinSet (ColimitObject Text (CGMorphism Text Text) Int)) (Function (ColimitObject Text (CGMorphism Text Text) Int)) (Set (ColimitObject Text (CGMorphism Text Text) Int)), NaturalTransformation (CompositionGraph Text Text) (CGMorphism Text Text) Text (FinSet (ColimitObject Text (CGMorphism Text Text) Int)) (Function (ColimitObject Text (CGMorphism Text Text) Int)) (Set (ColimitObject Text (CGMorphism Text Text) Int))) Source #
Computes the left Kan extension of a set-valued model to compute the pseudo-inverse of a function.
exampleSetValuedRightKanExtension :: (Diagram (CompositionGraph Text Text) (CGMorphism Text Text) Text (FinSet (LimitObject Text (CGMorphism Text Text) Int)) (Function (LimitObject Text (CGMorphism Text Text) Int)) (Set (LimitObject Text (CGMorphism Text Text) Int)), NaturalTransformation (CompositionGraph Text Text) (CGMorphism Text Text) Text (FinSet (LimitObject Text (CGMorphism Text Text) Int)) (Function (LimitObject Text (CGMorphism Text Text) Int)) (Set (LimitObject Text (CGMorphism Text Text) Int))) Source #
Computes the right Kan extension of a set-valued model to compute the pseudo-inverse of a function.