In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic...

like the strongly related notions of universal properties and adjoint functors, exist at a high level of abstraction. In order to understand them, it...

relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence between two related categories. Two functors that stand in...

up functor in Wiktionary, the free dictionary. A functor, in mathematics, is a map between categories. Functor may also refer to: Predicate functor in...

particularly homological algebra, an exact functor is a functor that preserves short exact sequences. Exact functors are convenient for algebraic calculations...

In functional programming, a functor is a design pattern inspired by the definition from category theory that allows one to apply a function to values...

is a fundamental result in category theory. It is an abstract result on functors of the type morphisms into a fixed object. It is a vast generalisation...

contravariant functor acts as a covariant functor from the opposite category Cop to D. A natural transformation is a relation between two functors. Functors often...

between objects) give rise to important functors to the category of sets. These functors are called hom-functors and have numerous applications in category...

a branch of mathematics, a functor category D C {\displaystyle D^{C}} is a category where the objects are the functors F : C → D {\displaystyle F:C\to...