In mathematics, specifically in category theory, an exponential object or map object is the categorical generalization of a function space in set theory...

standard form Exponential object, in category theory Exponential time, in complexity theory in probability and statistics: Exponential distribution, a...

Exponential object (category theory) Exponential polynomials—see also Touchard polynomials (combinatorics) Exponential response formula Exponential sheaf...

theory, however, [ A → B ] {\displaystyle [A\to B]} is known as the exponential object, and is written as B A {\displaystyle B^{A}} . There are other common...

}{N_{0}}}.} Exponential decay is a scalar multiple of the exponential distribution (i.e. the individual lifetime of each object is exponentially distributed)...

algebras, and the exponential object has the explicit form ¬ P ∨ Q {\displaystyle \neg P\lor Q} , thus making it clear that the exponential object really is material...

Object-oriented programming (OOP) is a programming paradigm based on the concept of objects. Objects can contain data (called fields, attributes or properties)...

in all programming languages. Cartesian closed category Currying Exponential object, category-theoretic equivalent First-class function Function space...

A digital object identifier (DOI) is a persistent identifier or handle used to uniquely identify various objects, standardized by the International Organization...

two objects A and B is given by the cartesian product A × B, the categorical sum is given by the disjoint union A + B, and the exponential object BA is...

morphism f {\displaystyle f} from some object A {\displaystyle A} to the exponential object B A {\displaystyle B^{A}} , then every endomorphism g : B → B {\displaystyle...

points correspond to equivariant maps X → Y; more generally, it is an exponential object in the category of G-sets. The notion of group action can be encoded...

category D C {\displaystyle D^{C}} has all the formal properties of an exponential object; in particular the functors from E × C → D {\displaystyle E\times...

time); In category theory, the function space is called an exponential object or map object. It appears in one way as the representation canonical bifunctor;...

of magmas Initial object Terminal object Zero object Subobject Group object Magma object Natural number object Exponential object Epimorphism Monomorphism...

theory, a branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C, there exists precisely one morphism...

2013. Harris, Derrick (18 April 2013). "Amazon S3 goes exponential, now stores 2 trillion objects". Gigaom. Retrieved 17 September 2013. Wilhelm, Alex (27...

the usual notation is B A {\displaystyle B^{A}} and this object is called the exponential object. Strictly speaking, we have defined a right closed monoidal...

and has an object Ω, called a subobject classifier. Although the term "power object" is sometimes used synonymously with exponential object YX, in topos...

product × {\displaystyle \times } , the object Y ⇒ Z {\displaystyle Y\Rightarrow Z} is called the exponential object, and is often written as Z Y {\displaystyle...

has as semantic interpretation the 0-tuple. Arity Coordinate vector Exponential object Formal language Multidimensional Expressions (OLAP) Prime k-tuple...

subobject classifier in Set. The power object of a set A is given by its power set, and the exponential object of the sets A and B is given by the set...

and exponential objects. A topos as defined above can be understood as a Cartesian closed category for which the notion of subobject of an object has...

A which assigns to each set the indiscrete category on that set. Exponential object. In a cartesian closed category the endofunctor C → C given by –×A...

ideas extend on the de Vries duality theorem. A definition of the exponential object is given below. Another suggestion (1964) was to consider the usual...

f\circ x=y} . If Y {\displaystyle Y} is an exponential object of the form B A {\displaystyle B^{A}} for some objects A , B {\displaystyle A,B} in C {\displaystyle...

JSON (JavaScript Object Notation, pronounced /ˈdʒeɪsən/ or /ˈdʒeɪˌsɒn/) is an open standard file format and data interchange format that uses human-readable...

cartesian closed (and therefore also not a topos) since it does not have exponential objects for all spaces. When this feature is desired, one often restricts...

parsers of XML documents. It is also referred to as an XML bomb or as an exponential entity expansion attack. The example attack consists of defining 10 entities...

of graphs is the category-theoretic product and the exponential graph is the exponential object for this category. Since these two operations are always...