Functors

AUTHORS:

• David Kohel and William Stein
• David Joyner (2005-12-17): examples
• Robert Bradshaw (2007-06-23): Pyrexify

sage.categories.functor.ForgetfulFunctor(domain, codomain)

Construct the forgetful function from one category to another.

EXAMPLES:

sage: rings = Rings()
sage: abgrps = CommutativeAdditiveGroups()
sage: F = ForgetfulFunctor(rings, abgrps)
sage: F
The forgetful functor from Category of rings to Category of commutative additive groups

class sage.categories.functor.ForgetfulFunctor_generic

Bases: sage.categories.functor.Functor

class sage.categories.functor.Functor

Bases: sage.structure.sage_object.SageObject

EXAMPLES:

sage: rings  = Rings()
sage: abgrps = CommutativeAdditiveGroups()
sage: F = ForgetfulFunctor(rings, abgrps)
sage: F.domain()
Category of rings
sage: F.codomain()
Category of commutative additive groups
sage: from sage.categories.functor import is_Functor
sage: is_Functor(F)
True
sage: I = IdentityFunctor(abgrps)
sage: I
The identity functor on Category of commutative additive groups
sage: I.domain()
Category of commutative additive groups
sage: is_Functor(I)
True

codomain()

domain()

sage.categories.functor.IdentityFunctor(C)

class sage.categories.functor.IdentityFunctor_generic

Bases: sage.categories.functor.ForgetfulFunctor_generic

sage.categories.functor.is_Functor(x)