What does functor mean?
In mathematics, particularly in category theory, a functor is a mapping between categories that preserves the structure of the categories. It is a way of transforming one mathematical structure into another while preserving the relationships between the elements. Functors are used to study the properties of mathematical structures and to construct new structures from old ones. The term functor is primarily used in mathematics and is a technical term with a specific meaning. It is not commonly used in everyday language. Functors have numerous applications in mathematics and computer science, including the study of algebraic structures, topological spaces, and programming languages.
A covariant functor is a functor that preserves the direction of morphisms.
"The covariant functor assigns to each vector space its dual space."
A contravariant functor is a functor that reverses the direction of morphisms.
"The contravariant functor assigns to each vector space its dual space."
The plural form functors is used when referring to multiple functors.
"The category of functors from C to D is denoted by Fun(C, D)."
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Etymology of functor
The term functor comes from the German word 'Funktor', which was introduced by mathematician Samuel Eilenberg in the 1940s. The term is derived from the word 'function', which is a fundamental concept in mathematics. The study of functors has led to significant advances in mathematics and computer science.
Usage notes
The term functor is primarily used in mathematics, particularly in category theory. It is a technical term with a specific meaning and is not commonly used in everyday language.