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ετυμολογία

Τι (ποιος) είναι injective functor - ορισμός

MODULE SUCH THAT INFINITE SYSTEMS OF LINEAR EQUATIONS CAN BE SOLVED BY SOLVING FINITE SUBSYSTEMS

Algebraically compact; Pure injective module; Pure-injective; Pure-injective module

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.

Βικιπαίδεια

Algebraically compact module

In mathematics, algebraically compact modules, also called pure-injective modules, are modules that have a certain "nice" property which allows the solution of infinite systems of equations in the module by finitary means. The solutions to these systems allow the extension of certain kinds of module homomorphisms. These algebraically compact modules are analogous to injective modules, where one can extend all module homomorphisms. All injective modules are algebraically compact, and the analogy between the two is made quite precise by a category embedding.

https://en.wikipedia.org/wiki/Algebraically compact module