Functor

class discopy.cat.Functor(ob, ar, ob_factory=None, ar_factory=None)

Bases: object

Defines a dagger functor which can be applied to objects and arrows.

By default, Functor defines an endofunctor from the free dagger category to itself. The codomain can be changed with the optional parameters ob_factory and ar_factory.

Parameters:

• ob (dict_like) – Mapping from cat.Ob to ob_factory.

• ar (dict_like) – Mapping from cat.Box to ar_factory.

• ob_factory (type, optional) – Class to be used as objects for the codomain of the functor. If None, this will be set to cat.Ob.

• ar_factory (type, optional) – Class to be used as arrows for the codomain of the functor. If None, this will be set to cat.Arrow.

Examples

>>> x, y, z = Ob('x'), Ob('y'), Ob('z')
>>> f, g = Box('f', x, y), Box('g', y, z)
>>> ob, ar = {x: y, y: z, z: y}, {f: g, g: g[::-1]}
>>> F = Functor(ob, ar)
>>> assert F(x) == y and F(f) == g

Notes

We can check the axioms of dagger functors.

>>> assert F(Id(x)) == Id(F(x))
>>> assert F(f >> g) == F(f) >> F(g)
>>> assert F(f[::-1]) == F(f)[::-1]
>>> assert F(f.dom) == F(f).dom and F(f.cod) == F(f).cod

Functors are bubble-preserving.

>>> assert F(f.bubble()) == F(f).bubble()

See also

Quiver

For functors from infinitely-generated categories, use quivers to create dict-like objects from functions.

property ob

Mapping on objects.

>>> F = Functor({Ob('x'): Ob('y')}, {})
>>> assert F.ob == {Ob('x'): Ob('y')}

property ar

Mapping on arrows.

>>> f, g = Box('f', Ob('x'), Ob('y')), Box('g', Ob('y'), Ob('z'))
>>> F = Functor({}, {f: g})
>>> assert F.ar == {f: g}