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30 relations: Adjoint functors, Cambridge University Press, Category (mathematics), Complete Boolean algebra, Complete lattice, Completeness (order theory), Dana Scott, Directed set, Distributivity (order theory), Dual (category theory), Equivalence of categories, Functor, Galois connection, General topology, Heyting algebra, Homomorphism, Lattice (order), Limit-preserving function (order theory), Mathematics, Monotonic function, Morphism, Open set, Order theory, Partially ordered set, Peter Johnstone (mathematician), Pointless topology, Power set, Scott continuity, Steve Vickers (computer scientist), Topological space.
Adjoint functors
In mathematics, specifically category theory, adjunction is a possible relationship between two functors.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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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.
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Complete Boolean algebra
In mathematics, a complete Boolean algebra is a Boolean algebra in which every subset has a supremum (least upper bound).
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Complete lattice
In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet).
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Completeness (order theory)
In the mathematical area of order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set (poset).
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Dana Scott
Dana Stewart Scott (born October 11, 1932) is the emeritus Hillman University Professor of Computer Science, Philosophy, and Mathematical Logic at Carnegie Mellon University; he is now retired and lives in Berkeley, California.
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Directed set
In mathematics, a directed set (or a directed preorder or a filtered set) is a nonempty set A together with a reflexive and transitive binary relation ≤ (that is, a preorder), with the additional property that every pair of elements has an upper bound.
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Distributivity (order theory)
In the mathematical area of order theory, there are various notions of the common concept of distributivity, applied to the formation of suprema and infima.
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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.
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Equivalence of categories
In category theory, an abstract branch of mathematics, an equivalence of categories is a relation between two categories that establishes that these categories are "essentially the same".
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Functor
In mathematics, a functor is a map between categories.
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Galois connection
In mathematics, especially in order theory, a Galois connection is a particular correspondence (typically) between two partially ordered sets (posets).
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General topology
In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology.
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Heyting algebra
In mathematics, a Heyting algebra is a bounded lattice (with join and meet operations written ∨ and ∧ and with least element 0 and greatest element 1) equipped with a binary operation a → b of implication such that c ∧ a ≤ b is equivalent to c ≤ a → b. From a logical standpoint, A → B is by this definition the weakest proposition for which modus ponens, the inference rule A → B, A ⊢ B, is sound.
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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).
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Lattice (order)
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.
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Limit-preserving function (order theory)
In the mathematical area of order theory, one often speaks about functions that preserve certain limits, i.e. certain suprema or infima.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Monotonic function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.
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Morphism
In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.
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Open set
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
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Order theory
Order theory is a branch of mathematics which investigates the intuitive notion of order using binary relations.
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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.
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Peter Johnstone (mathematician)
Peter Tennant Johnstone (born 1948) is Professor of the Foundations of Mathematics at the University of Cambridge, and a fellow of St. John's College.
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Pointless topology
In mathematics, pointless topology (also called point-free or pointfree topology, or locale theory) is an approach to topology that avoids mentioning points.
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Power set
In mathematics, the power set (or powerset) of any set is the set of all subsets of, including the empty set and itself, variously denoted as, 𝒫(), ℘() (using the "Weierstrass p"),,, or, identifying the powerset of with the set of all functions from to a given set of two elements,.
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Scott continuity
In mathematics, given two partially ordered sets P and Q, a function f \colon P \rightarrow Q between them is Scott-continuous (named after the mathematician Dana Scott) if it preserves all directed suprema, i.e. if for every directed subset D of P with supremum in P its image has a supremum in Q, and that supremum is the image of the supremum of D: that is, \sqcup f.
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Steve Vickers (computer scientist)
Steve Vickers (born c. 1953) is a British mathematician and computer scientist.
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Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
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Category of frames, Complete heyting algebra, Frame (order theory), Frame homomorphism, Frames and locales, Locale (mathematics).
References
[1] https://en.wikipedia.org/wiki/Complete_Heyting_algebra
