Functor Morphism

An Functor Morphism is a morphism between category entities.

• AKA: Endofunctor, Category Homomorphism.
  • …
• Counter-Example(s):
  • a Continuous Function.
• See: Category (Mathematics), Category Theory, Homomorphism, Category of Small Categories, Algebraic Topology, Fundamental Group, Topological Space, Linguistics.

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References

2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/functor Retrieved:2014-4-24.
  • In mathematics, a functor is a type of mapping between categories, which is applied in category theory. Functors can be thought of as homomorphisms between categories. In the category of small categories, functors can be thought of more generally as morphisms.

    Functors were first considered in algebraic topology, where algebraic objects (like the fundamental group) are associated to topological spaces, and algebraic homomorphisms are associated to continuous maps. Nowadays, functors are used throughout modern mathematics to relate various categories. Thus, functors are generally applicable in areas within mathematics that category theory can make an abstraction of.

    The word functor was borrowed by mathematicians from the philosopher Rudolf Carnap, who used the term in a linguistic context:

    see function word.

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