| Copyright | Guillaume Sabbagh 2022 |
|---|---|
| License | GPL-3 |
| Maintainer | guillaumesabbagh@protonmail.com |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | Safe-Inferred |
| Language | Haskell2010 |
Math.Functors.DiagonalFunctor
Description
The diagonal functor sends each object to the constant functor on this object.
Synopsis
- diagonalFunctor :: (FiniteCategory c1 m1 o1, Morphism m1 o1, FiniteCategory c2 m2 o2, Morphism m2 o2) => c1 -> c2 -> Diagram c2 m2 o2 (FunctorCategory c1 m1 o1 c2 m2 o2) (NaturalTransformation c1 m1 o1 c2 m2 o2) (Diagram c1 m1 o1 c2 m2 o2)
Documentation
Arguments
| :: (FiniteCategory c1 m1 o1, Morphism m1 o1, FiniteCategory c2 m2 o2, Morphism m2 o2) | |
| => c1 | J |
| -> c2 | C |
| -> Diagram c2 m2 o2 (FunctorCategory c1 m1 o1 c2 m2 o2) (NaturalTransformation c1 m1 o1 c2 m2 o2) (Diagram c1 m1 o1 c2 m2 o2) | D : C -> C^J |
Given two categories J and C, return the diagonal functor C -> C^J.
Let J and C be two categories, we consider the functor category C^J. The diagonal functor D : C -> C^J maps each object x of C to the constant diagram D_x from J to C. It maps each morphism to the natural transformation between the two constant diagrams associated to the source and the target of the morphism.