Faster access than browser!
53 relations: Abelian group, Ackermann function, Actual infinity, Algebra over a field, Algebraic data type, Associative property, Catamorphism, Category (mathematics), Category of sets, Category theory, Charity (programming language), Coinduction, Computability theory, Coproduct, Data structure, Differentiable manifold, Disjoint union, Domain (ring theory), Dual (category theory), Duality (mathematics), F-coalgebra, Field (mathematics), Finite set, Functor, Group (mathematics), Group object, Homomorphism, Identity element, Initial and terminal objects, Inverse element, Lattice (order), Least fixed point, List (abstract data type), Lookup table, Mathematical optimization, Mathematics, Module (mathematics), Monad (category theory), Monoid, Monoid (category theory), Morphism, Natural number, Normalization property (abstract rewriting), Parametricity, Partially ordered set, Ring (mathematics), Scalar multiplication, Semigroup, Smoothness, Subobject classifier, ..., Total order, Universal algebra, Vector space. Expand index (3 more) »
Abelian group
In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.
New!!: F-algebra and Abelian group · See more »
Ackermann function
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive.
New!!: F-algebra and Ackermann function · See more »
Actual infinity
In the philosophy of mathematics, the abstraction of actual infinity involves the acceptance (if the axiom of infinity is included) of infinite entities, such as the set of all natural numbers or an infinite sequence of rational numbers, as given, actual, completed objects.
New!!: F-algebra and Actual infinity · See more »
Algebra over a field
In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product.
New!!: F-algebra and Algebra over a field · See more »
Algebraic data type
In computer programming, especially functional programming and type theory, an algebraic data type is a kind of composite type, i.e., a type formed by combining other types.
New!!: F-algebra and Algebraic data type · See more »
Associative property
In mathematics, the associative property is a property of some binary operations.
New!!: F-algebra and Associative property · See more »
Catamorphism
In category theory, the concept of catamorphism (from the Greek: κατά "downwards" and μορφή "form, shape") denotes the unique homomorphism from an initial algebra into some other algebra.
New!!: F-algebra and Catamorphism · See more »
Category (mathematics)
In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is an algebraic structure similar to a group but without requiring inverse or closure properties.
New!!: F-algebra and Category (mathematics) · See more »
Category of sets
In the mathematical field of category theory, the category of sets, denoted as Set, is the category whose objects are sets.
New!!: F-algebra and Category of sets · See more »
Category theory
Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).
New!!: F-algebra and Category theory · See more »
Charity (programming language)
Charity is an experimental purely functional programming language, developed at the University of Calgary under the supervision of Robin Cockett.
New!!: F-algebra and Charity (programming language) · See more »
Coinduction
In computer science, coinduction is a technique for defining and proving properties of systems of concurrent interacting objects.
New!!: F-algebra and Coinduction · See more »
Computability theory
Computability theory, also known as recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.
New!!: F-algebra and Computability theory · See more »
Coproduct
In category theory, the coproduct, or categorical sum, is a category-theoretic construction which includes as examples the disjoint union of sets and of topological spaces, the free product of groups, and the direct sum of modules and vector spaces.
New!!: F-algebra and Coproduct · See more »
Data structure
In computer science, a data structure is a data organization and storage format that enables efficient access and modification.
New!!: F-algebra and Data structure · See more »
Differentiable manifold
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.
New!!: F-algebra and Differentiable manifold · See more »
Disjoint union
In set theory, the disjoint union (or discriminated union) of a family of sets is a modified union operation that indexes the elements according to which set they originated in.
New!!: F-algebra and Disjoint union · See more »
Domain (ring theory)
In mathematics, and more specifically in algebra, a domain is a nonzero ring in which implies or.
New!!: F-algebra and Domain (ring theory) · See more »
Dual (category theory)
In category theory, a branch of mathematics, duality is a correspondence between the properties of a category C and the dual properties of the opposite category Cop.
New!!: F-algebra and Dual (category theory) · See more »
Duality (mathematics)
In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. Such involutions sometimes have fixed points, so that the dual of A is A itself.
New!!: F-algebra and Duality (mathematics) · See more »
F-coalgebra
In mathematics, specifically in category theory, an F-coalgebra is a structure defined according to a functor F. For both algebra and coalgebra, a functor is a convenient and general way of organizing a signature.
New!!: F-algebra and F-coalgebra · See more »
Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
New!!: F-algebra and Field (mathematics) · See more »
Finite set
In mathematics, a finite set is a set that has a finite number of elements.
New!!: F-algebra and Finite set · See more »
Functor
In mathematics, a functor is a map between categories.
New!!: F-algebra and Functor · See more »
Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
New!!: F-algebra and Group (mathematics) · See more »
Group object
In category theory, a branch of mathematics, group objects are certain generalizations of groups which are built on more complicated structures than sets.
New!!: F-algebra and Group object · See more »
Homomorphism
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces).
New!!: F-algebra and Homomorphism · See more »
Identity element
In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them.
New!!: F-algebra and Identity element · See more »
Initial and terminal objects
In category 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 I → X. The dual notion is that of a terminal object (also called terminal element): T is terminal if for every object X in C there exists a single morphism X → T. Initial objects are also called coterminal or universal, and terminal objects are also called final.
New!!: F-algebra and Initial and terminal objects · See more »
Inverse element
In abstract algebra, the idea of an inverse element generalises concepts of a negation (sign reversal) in relation to addition, and a reciprocal in relation to multiplication.
New!!: F-algebra and Inverse element · See more »
Lattice (order)
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.
New!!: F-algebra and Lattice (order) · See more »
Least fixed point
In order theory, a branch of mathematics, the least fixed point (lfp or LFP, sometimes also smallest fixed point) of a function from a partially ordered set to itself is the fixed point which is less than each other fixed point, according to the set's order.
New!!: F-algebra and Least fixed point · See more »
List (abstract data type)
In computer science, a list or sequence is an abstract data type that represents a countable number of ordered values, where the same value may occur more than once.
New!!: F-algebra and List (abstract data type) · See more »
Lookup table
In computer science, a lookup table is an array that replaces runtime computation with a simpler array indexing operation.
New!!: F-algebra and Lookup table · See more »
Mathematical optimization
In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.
New!!: F-algebra and Mathematical optimization · See more »
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
New!!: F-algebra and Mathematics · See more »
Module (mathematics)
In mathematics, a module is one of the fundamental algebraic structures used in abstract algebra.
New!!: F-algebra and Module (mathematics) · See more »
Monad (category theory)
In category theory, a branch of mathematics, a monad (also triple, triad, standard construction and fundamental construction) is an endofunctor (a functor mapping a category to itself), together with two natural transformations.
New!!: F-algebra and Monad (category theory) · See more »
Monoid
In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element.
New!!: F-algebra and Monoid · See more »
Monoid (category theory)
In category theory, a monoid (or monoid object) (M, μ, η) in a monoidal category (C, ⊗, I) is an object M together with two morphisms.
New!!: F-algebra and Monoid (category theory) · See more »
Morphism
In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.
New!!: F-algebra and Morphism · See more »
Natural number
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
New!!: F-algebra and Natural number · See more »
Normalization property (abstract rewriting)
In mathematical logic and theoretical computer science, a rewrite system has the (strong) normalization property or is terminating if every term is strongly normalizing; that is, if every sequence of rewrites eventually terminates with an irreducible term, also called a normal form.
New!!: F-algebra and Normalization property (abstract rewriting) · See more »
Parametricity
In programming language theory, parametricity is an abstract uniformity property enjoyed by parametrically polymorphic functions, which captures the intuition that all instances of a polymorphic function act the same way.
New!!: F-algebra and Parametricity · See more »
Partially ordered set
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.
New!!: F-algebra and Partially ordered set · See more »
Ring (mathematics)
In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.
New!!: F-algebra and Ring (mathematics) · See more »
Scalar multiplication
In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra).
New!!: F-algebra and Scalar multiplication · See more »
Semigroup
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation.
New!!: F-algebra and Semigroup · See more »
Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
New!!: F-algebra and Smoothness · See more »
Subobject classifier
In category theory, a subobject classifier is a special object Ω of a category such that, intuitively, the subobjects of any object X in the category correspond to the morphisms from X to Ω. In typical examples, that morphism assigns "true" to the elements of the subobject and "false" to the other elements of X. Therefore a subobject classifier is also known as a "truth value object" and the concept is widely used in the categorical description of logic.
New!!: F-algebra and Subobject classifier · See more »
Total order
In mathematics, a linear order, total order, simple order, or (non-strict) ordering is a binary relation on some set X, which is antisymmetric, transitive, and a connex relation.
New!!: F-algebra and Total order · See more »
Universal algebra
Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures.
New!!: F-algebra and Universal algebra · See more »
Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
New!!: F-algebra and Vector space · See more »
Redirects here:
Algebra for an endofunctor, F algebra.
References
[1] https://en.wikipedia.org/wiki/F-algebra
