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Posetal category

In mathematics, specifically category theory, a posetal category, or thin category, is a category whose homsets each contain at most one morphism. As such, a posetal category amounts to a preordered class. As suggested by the name, the further re ...

Product category

In the mathematical field of category theory, the product of two categories C and D, denoted C × D and called a product category, is an extension of the concept of the Cartesian product of two sets. Product categories are used to define bifunctor ...

Pseudo-abelian category

In mathematics, specifically in category theory, a pseudo-abelian category is a category that is preadditive and is such that every idempotent has a kernel. Recall that an idempotent morphism p {\displaystyle p} is an endomorphism of an object wi ...

Quantaloid

In mathematics, a quantaloid is a category enriched over the category Sup of suplattices. In other words for any objects a, b the morphism object between them is not just a set but a complete lattice, in such a way that composition of morphisms p ...

Quotient category

In mathematics, a quotient category is a category obtained from another one by identifying sets of morphisms. Formally, it is a quotient object in the category of categories, analogous to a quotient group or quotient space, but in the categorical ...

Quotient of an abelian category

In mathematics, the quotient of an abelian category A {\displaystyle {\mathcal {A}}} by a Serre subcategory B {\displaystyle {\mathcal {B}}} is the abelian category A / B {\displaystyle {\mathcal {A}}/{\mathcal {B}}} which, intuitively, is obtain ...

Section (category theory)

In category theory, a branch of mathematics, a section is a right inverse of some morphism. Dually, a retraction is a left inverse of some morphism. In other words, if f: X → Y and g: Y → X are morphisms whose composition f o g: Y → Y is the iden ...

Seifert–van Kampen theorem

In mathematics, the Seifert–van Kampen theorem of algebraic topology, sometimes just called van Kampens theorem, expresses the structure of the fundamental group of a topological space X {\displaystyle X} in terms of the fundamental groups of two ...

Sieve (category theory)

In category theory, a branch of mathematics, a sieve is a way of choosing arrows with a common codomain. It is a categorical analogue of a collection of open subsets of a fixed open set in topology. In a Grothendieck topology, certain sieves beco ...

Simplicially enriched category

In mathematics, a simplicially enriched category, is a category enriched over the category of simplicial sets. Simplicially enriched categories are often also called, more ambiguously, simplicial categories ; the latter term however also applies ...

Skeleton (category theory)

In mathematics, a skeleton of a category is a subcategory that, roughly speaking, does not contain any extraneous isomorphisms. In a certain sense, the skeleton of a category is the "smallest" equivalent category, which captures all "categorical ...

Stable model category

In category theory, a branch of mathematics, a stable model category is a pointed model category in which the suspension functor is an equivalence of the homotopy category with itself. The prototypical examples are the category of spectra in the ...

Structure (category theory)

In mathematics, progress often consists of recognizing the same structure in different contexts, so one way to use it has several applications. Actually this is a normal way of production, in the absence of a recognizable frame problems usually f ...

Topological category

In category theory, a discipline in mathematics, the notion of topological category has a number of different, inequivalent definitions. In one approach, a topological category is a category that is enriched over the category of compactly generat ...

Tower (mathematics)

In category theory, a branch of abstract mathematics, a tower is defined as follows. Let I {\displaystyle {\mathcal {I}}} be the poset ⋯ → 2 → 1 → 0 {\displaystyle \cdots \rightarrow 2\rightarrow 1\rightarrow 0} of whole numbers in reverse order, ...

Waldhausen category

In mathematics, a Waldhausen category is a category C equipped with some additional data, which makes it possible to construct the K-theory spectrum of C using a so-called S-construction. Its named after Friedhelm Waldhausen, who introduced this ...

Argumentum ad crumenam

An argumentum ad crumenam argument, also known as an argument to the purse, is the informal fallacy of concluding that a statement is correct because the speaker is rich. The opposite is the argumentum ad lazarum.

Argumentum ad lazarum

Argumentum ad lazarum or appeal to poverty is the informal fallacy of thinking a conclusion is correct solely because the speaker is poor, or it is incorrect because the speaker is rich. It is named after Lazarus, a beggar in a New Testament para ...

Consequentia mirabilis

Consequentia mirabilis, also known as Claviuss Law, is used in traditional and classical logic to establish the truth of a proposition from the inconsistency of its negation. It is thus similar to reductio ad absurdum, but it can prove a proposit ...

Secundum quid

Secundum quid is a type of informal fallacy that occurs when the arguer fails to recognize the difference between rules of thumb and categorical propositions, rules that hold true universally. Since it ignores the limits, or qualifications, of ru ...

Modal scope fallacy

a) Bachelors are necessarily unmarried. b) John is a bachelor. Therefore, c) John cannot marry. The condition a) appears to be a tautology and therefore true. The condition b) is a statement of fact about John which makes him subject to a); that ...

Double bubble conjecture

In the mathematical theory of minimal surfaces, the double bubble conjecture states that the shape that encloses and separates two given volumes and has the minimum possible surface area is a standard double bubble - three spherical surfaces meet ...

Thom conjecture

In mathematics, a smooth algebraic curve C {\displaystyle C} in the complex projective plane, of degree d {\displaystyle d}, has genus given by the genus–degree formula g = d − 1 d − 2 / 2 {\displaystyle g=d-1d-2/2}. The Thom conjecture, named af ...

Conditional quantum entropy

The conditional quantum entropy is an entropy measure used in quantum information theory. It is a generalization of the conditional entropy of classical information theory. For a bipartite state ρ A B {\displaystyle \rho ^{AB}}, the conditional e ...

Generalized relative entropy

Generalized relative entropy is a measure of dissimilarity between two quantum states. It is a "one-shot" analogue of quantum relative entropy and shares many properties of the latter quantity. In the study of quantum information theory, we typic ...

Lieb conjecture

In quantum information theory, the Lieb conjecture is a theorem concerning the Wehrl entropy of quantum systems for which the classical phase space is a sphere. It states that no state of such a system has a lower Wehrl entropy than the SU cohere ...

Min-entropy

The min-entropy, in information theory, is the smallest of the Renyi family of entropies, corresponding to the most conservative way of measuring the unpredictability of a set of outcomes, as the negative logarithm of the probability of the most ...

Bucket queue

In the design and analysis of data structures, a bucket queue is a priority queue for prioritizing elements whose priorities are small integers. It has the form of an array of buckets: an array data structure, indexed by the priorities, whose cel ...

Calendar queue

A calendar queue is a priority queue. It is analogous to desk calendar, which is used by humans for ordering future events by date. Discrete event simulations require a future event list structure that sorts pending events according to their time ...

Leftist tree

In computer science, a leftist tree or leftist heap is a priority queue implemented with a variant of a binary heap. Every node x has an s-value which is the distance to the nearest leaf in subtree rooted at x. In contrast to a binary heap, a lef ...

Min-max heap

In computer science, a min-max heap is a complete binary tree data structure which combines the usefulness of both a min-heap and a max-heap, that is, it provides constant time retrieval and logarithmic time removal of both the minimum and maximu ...

Monotone priority queue

In computer science, a monotone priority queue is a variant of the priority queue abstract data type in which the priorities of extracted items are required to form a monotonic sequence. That is, for a priority queue in which each successively ex ...

Pagoda (data structure)

In computer science, a pagoda is a priority queue implemented with a variant of a binary tree. The root points to its children, as in a binary tree. Every other node points back to its parent and down to its leftmost or rightmost descendant leaf. ...

Randomized meldable heap

In computer science, a randomized meldable heap is a priority queue based data structure in which the underlying structure is also a heap-ordered binary tree. However, there are no restrictions on the shape of the underlying binary tree. This app ...

Van Emde Boas tree

A van Emde Boas tree, also known as a vEB tree or van Emde Boas priority queue, is a tree data structure which implements an associative array with m -bit integer keys. It performs all operations in O time, or equivalently in O time, where M = 2 ...

C++ classes

A class in C++ is a user-defined type or data structure declared with keyword class that has data and functions as its members whose access is governed by the three access specifiers private, protected or public. By default access to members of a ...

Class browser

A class browser is a feature of an integrated development environment that allows the programmer to browse, navigate, or visualize the structure of object-oriented programming code.

Class hierarchy

This article is about the computer science concept. For the sociology concept, please see social class. A class hierarchy or inheritance tree in computer science is a classification of object types, denoting objects as the instantiations of class ...

Class implementation file

In object-oriented programming, a class implementation file is often used to contain the implementation code for the method of a class. This file is also referred to as a source file. Programming languages like C and C++ make use of these impleme ...

Class invariant

In computer programming, specifically object-oriented programming, a class invariant is an invariant used for constraining objects of a class. Methods of the class should preserve the invariant. The class invariant constrains the state stored in ...

Downcasting

In class-based programming, downcasting or type refinement is the act of casting a reference of a base class to one of its derived classes. In many programming languages, it is possible to check through type introspection to determine whether the ...

Fragile base class

The fragile base class problem is a fundamental architectural problem of object-oriented programming systems where base classes are considered "fragile" because seemingly safe modifications to a base class, when inherited by the derived classes, ...

Friend class

A friend class in C++ can access the private and protected members of the class in which it is declared as a friend. A significant use of a friend class is for a part of a data structure, represented by a class, to provide access to the main clas ...

Helper class

In object-oriented programming, a helper class is used to assist in providing some functionality, which isnt the main goal of the application or class in which it is used. An instance of a helper class is called a helper object. Helper classes ar ...

Metaclass

In object-oriented programming, a metaclass is a class whose instances are classes. Just as an ordinary class defines the behavior of certain objects, a metaclass defines the behavior of certain classes and their instances. Not all object-oriente ...

Multiple inheritance

Multiple inheritance is a feature of some object-oriented computer programming languages in which an object or class can inherit characteristics and features from more than one parent object or parent class. It is distinct from single inheritance ...

Run-time type information

In computer programming, run-time type information or run-time type identification is a feature of the C++ programming language that exposes information about an objects data type at runtime. Run-time type information can apply to simple data typ ...

Virtual inheritance

Virtual inheritance is a C++ technique that ensures only one copy of a base class s member variables are inherited by grandchild derived classes. Without virtual inheritance, if two classes B and C inherit from a class A, and a class D inherits f ...

Abstract graphical data type

An abstract graphical data type is an extension of an abstract data type for computer graphics. AGDTs provide the advantages of the ADTs with facilities to build graphical objects in a structured way. Formally, an AGDT may be defined as a "class ...

Address constant

In IBM System/360 through present day z/Architecture, an address constant or "adcon" is an assembly language data type which contains the address of a location in computer memory. An address constant can be one, two, three or four bytes long, alt ...