# Categorical

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**Background and genesis of topos theory**— This page gives some very general background to the mathematical idea of topos. This is an aspect of category theory, and has a reputation for being abstruse. The level of abstraction involved cannot be reduced beyond a certain point; but on the… …182

**Opinion poll**— An opinion poll, sometimes simply referred to as a poll is a survey of public opinion from a particular sample. Opinion polls are usually designed to represent the opinions of a population by conducting a series of questions and then… …183

**Löwenheim–Skolem theorem**— In mathematical logic, the Löwenheim–Skolem theorem, named for Leopold Löwenheim and Thoralf Skolem, states that if a countable first order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ. The… …184

**Monad (category theory)**— For the uses of monads in computer software, see monads in functional programming. In category theory, a branch of mathematics, a monad, Kleisli triple, or triple is an (endo )functor, together with two natural transformations. Monads are used in …185

**Order theory**— For a topical guide to this subject, see Outline of order theory. Order theory is a branch of mathematics which investigates our intuitive notion of order using binary relations. It provides a formal framework for describing statements such as… …186

**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 . There are numerous examples of categorical equivalences… …187

**Cyclic order**— In mathematics, a cyclic order is a way to arrange a set of objects in a circle.[nb] Unlike most structures in order theory, a cyclic order cannot be modeled as a binary relation a < b . One does not say that east is more clockwise than west.… …188

**Category of topological spaces**— In mathematics, the category of topological spaces, often denoted Top, is the category whose objects are topological spaces and whose morphisms are continuous maps. This is a category because the composition of two continuous maps is again… …189

**Interaction (statistics)**— In statistics, an interaction is a term in a statistical model added when the effect of two or more variables is not simply additive. Such a term reflects that the effect of one variable depends on the values of one or more other variables. Thus …190

**Decision tree learning**— This article is about decision trees in machine learning. For the use of the term in decision analysis, see Decision tree. Decision tree learning, used in statistics, data mining and machine learning, uses a decision tree as a predictive model… …191

**Clean Water Act**— For Clean Water Act of Ontario, Canada, see Clean Water Act (Ontario). Clean Water Act Full title Federal Water Pollution Control Amendments of 1972 Acronym CWA / Clean Water Act Enacted by the 92nd United …192

**Complete Heyting algebra**— In mathematics, especially in order theory, a complete Heyting algebra is a Heyting algebra which is complete as a lattice. Complete Heyting algebras are the objects of three different categories; the category CHey, the category Loc of locales,… …193

**Fallacy of four terms**— The fallacy of four terms (Latin: quaternio terminorum ) is the logical fallacy that occurs when a categorical syllogism has four terms.Valid categorical syllogisms always have three terms::Major premise: All fish have fins.:Minor premise: All… …194

**Fisher's exact test**— is a statistical significance test used in the analysis of categorical data where sample sizes are small. It is named after its inventor, R. A. Fisher, and is one of a class of exact tests. Fisher devised the test following a comment from Muriel… …195

**Level of measurement**— The levels of measurement , or scales of measure are expressions that typically refer to the theory of scale types developed by the psychologist Stanley Smith Stevens. Stevens proposed his theory in a 1946 Science article titled On the theory of… …196

**William Lawvere**— Francis William Lawvere (b. February 9, 1937 in Muncie, Indiana) is a mathematician known for his work in category theory, topos theory and the philosophy of mathematics.BiographyBorn February 9, 1937 in Muncie, Indiana, Lawvere studied continuum …197

**Skolem's paradox**— is the mathematical fact that every countable axiomatisation of set theory in first order logic, if consistent, has a model that is countable, even if it is possible to prove, from those same axioms, the existence of sets that are not countable.… …198

**Computer ethics**— is a branch of practical philosophy which deals with how computing professionals should make decisions regarding professional and social conduct.[1] Margaret Anne Pierce, a professor in the Department of Mathematics and Computers at Georgia… …199

**Cohen's kappa**— coefficient is a statistical measure of inter rater agreement or inter annotator agreement[1] for qualitative (categorical) items. It is generally thought to be a more robust measure than simple percent agreement calculation since κ takes into… …200

**Fibred category**— Fibred categories are abstract entities in mathematics used to provide a general framework for descent theory. They formalise the various situations in geometry and algebra in which inverse images (or pull backs) of objects such as vector bundles …