| Copyright | Guillaume Sabbagh 2022 |
|---|---|
| License | GPL-3 |
| Maintainer | guillaumesabbagh@protonmail.com |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | Safe-Inferred |
| Language | Haskell2010 |
Math.Functors.Adjunction
Description
Adjunctions are all over the place in mathematics. Note that leftAdjoint and rightAdjoint are slow because we enumerate a lot of morphisms to find the universal morphisms. Prefer using your own construction of an adjoint if known.
Synopsis
- leftAdjoint :: (FiniteCategory c1 m1 o1, Morphism m1 o1, Eq m1, Eq o1, FiniteCategory c2 m2 o2, Morphism m2 o2, Eq m2, Eq o2) => Diagram c1 m1 o1 c2 m2 o2 -> Diagram c2 m2 o2 c1 m1 o1
- rightAdjoint :: (FiniteCategory c1 m1 o1, Morphism m1 o1, Eq m1, Eq o1, FiniteCategory c2 m2 o2, Morphism m2 o2, Eq m2, Eq o2) => Diagram c2 m2 o2 c1 m1 o1 -> Diagram c1 m1 o1 c2 m2 o2
Documentation
leftAdjoint :: (FiniteCategory c1 m1 o1, Morphism m1 o1, Eq m1, Eq o1, FiniteCategory c2 m2 o2, Morphism m2 o2, Eq m2, Eq o2) => Diagram c1 m1 o1 c2 m2 o2 -> Diagram c2 m2 o2 c1 m1 o1 Source #
Returns the left adjoint of a functor, if the left adjoint does not exist, returns a partial Diagram being the best ajoint we could construct.
Note that leftAdjoint and rightAdjoint are slow because we enumerate a lot of morphisms to find the universal morphisms. Prefer using your own construction of an adjoint if known.
rightAdjoint :: (FiniteCategory c1 m1 o1, Morphism m1 o1, Eq m1, Eq o1, FiniteCategory c2 m2 o2, Morphism m2 o2, Eq m2, Eq o2) => Diagram c2 m2 o2 c1 m1 o1 -> Diagram c1 m1 o1 c2 m2 o2 Source #
Returns the right adjoint of a functor, if the right adjoint does not exist, returns a partial Diagram being the best ajoint we could construct.
Note that leftAdjoint and rightAdjoint are slow because we enumerate a lot of morphisms to find the universal morphisms. Prefer using your own construction of an adjoint if known.