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What (who) is homotopy functor - definition

VALUE OF A LEFT ADJOINT FUNCTOR TO A FORGETFUL FUNCTOR

Free functor; Cofree functor

Functor

IN CATEGORY THEORY, A MAPPING BETWEEN CATEGORIES THAT PRESERVES THEIR STRUCTURE (IDENTITY MORPHISMS, COMPOSITION OF MORPHISMS)

Covariant functor; Contravariant functor; Cofunctor; Functorial; Functors; Functoriality; Endofunctor; Bifunctor; Covariance and contravariance of functors; Identity functor; Multifunctor; Functor (category theory); Covariance (categories); Opposite functor; Constant functor; Selection functor; Category homomorphism; Dual functor; Covariance and contravariance (category theory)

In mathematics, specifically category theory, a functor is a [between categories]. Functors were first considered in [[algebraic topology, where algebraic objects (such as the fundamental group) are associated to topological spaces, and maps between these algebraic objects are associated to continuous maps between spaces.

https://en.wikipedia.org/wiki/Functor

functor

IN CATEGORY THEORY, A MAPPING BETWEEN CATEGORIES THAT PRESERVES THEIR STRUCTURE (IDENTITY MORPHISMS, COMPOSITION OF MORPHISMS)

Covariant functor; Contravariant functor; Cofunctor; Functorial; Functors; Functoriality; Endofunctor; Bifunctor; Covariance and contravariance of functors; Identity functor; Multifunctor; Functor (category theory); Covariance (categories); Opposite functor; Constant functor; Selection functor; Category homomorphism; Dual functor; Covariance and contravariance (category theory)

In category theory, a functor F is an operator on types. F is also considered to be a polymorphic operator on functions with the type F : (a -> b) -> (F a -> F b). Functors are a generalisation of the function "map". The type operator in this case takes a type T and returns type "list of T". The map function takes a function and applies it to each element of a list. (1995-02-07)

functor

IN CATEGORY THEORY, A MAPPING BETWEEN CATEGORIES THAT PRESERVES THEIR STRUCTURE (IDENTITY MORPHISMS, COMPOSITION OF MORPHISMS)

Covariant functor; Contravariant functor; Cofunctor; Functorial; Functors; Functoriality; Endofunctor; Bifunctor; Covariance and contravariance of functors; Identity functor; Multifunctor; Functor (category theory); Covariance (categories); Opposite functor; Constant functor; Selection functor; Category homomorphism; Dual functor; Covariance and contravariance (category theory)

['f??kt?]

¦ noun Logic & Mathematics a function; an operator.

Wikipedia

Free object

In mathematics, the idea of a free object is one of the basic concepts of abstract algebra. Informally, a free object over a set A can be thought of as being a "generic" algebraic structure over A: the only equations that hold between elements of the free object are those that follow from the defining axioms of the algebraic structure. Examples include free groups, tensor algebras, or free lattices.

The concept is a part of universal algebra, in the sense that it relates to all types of algebraic structure (with finitary operations). It also has a formulation in terms of category theory, although this is in yet more abstract terms.

https://en.wikipedia.org/wiki/Free object