Module: sage.categories.functor
Functors
Author: - David Kohel and William Stein - David Joyner (2005-12-17): examples - Robert Bradshaw (2007-06-23): Pyrexify
Module-level Functions
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Construct the forgetful function from one category to another.
sage: rings = Rings() sage: abgrps = AbelianGroups() sage: F = ForgetfulFunctor(rings, abgrps) sage: F The forgetful functor from Rings to AbelianGroups
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Class: ForgetfulFunctor_generic
Special Functions: __cmp__,
__reduce__,
__repr__,
_apply_functor
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sage: F = ForgetfulFunctor(Groups(), Sets()) sage: loads(F.dumps()) == F True
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Class: Functor
sage: rings = Rings() sage: abgrps = AbelianGroups() sage: F = ForgetfulFunctor(rings, abgrps) sage: F.domain() Category of rings sage: F.codomain() Category of abelian groups sage: is_Functor(F) True sage: I = IdentityFunctor(abgrps) sage: I The identity functor on AbelianGroups sage: I.domain() Category of abelian groups sage: is_Functor(I) True
Functions: codomain,
domain
Special Functions: __call__,
__init__,
__repr__
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Class: IdentityFunctor_generic
Special Functions: __call__,
__init__,
__reduce__,
__repr__,
_apply_functor
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sage: F = IdentityFunctor(Groups()) sage: loads(F.dumps()) == F True
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