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Что (кто) такое category theory - определение
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Category theory
BRANCH OF MATHEMATICS STUDYING CATEGORIES, FUNCTORS, AND NATURAL TRANSFORMATIONS
CategoryTheory; Category Theory; Category theoretic; Category-theoretic; Categorical point of view; Draft:Applied Category Theory; Object of a category
Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, category theory is used in almost all areas of mathematics, and in some areas of computer science.
Outline of category theory
OVERVIEW OF AND TOPICAL GUIDE TO CATEGORY THEORY
List of category theory topics
The following outline is provided as an overview of and guide to category theory, the area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows (also called morphisms, although this term also has a specific, non category-theoretical sense), where these collections satisfy certain basic conditions. Many significant areas of mathematics can be formalised as categories, and the use of category theory allows many intricate and subtle mathematical results in these fields to be stated, and proved, in a much simpler way than without the use of categories.
Category of medial magmas
CATEGORY IN MATHEMATICS
Medial category; Med (category theory)
In mathematics, the category of medial magmas, also known as the medial category, and denoted Med, is the category whose objects are medial magmas (that is, sets with a medial binary operation), and whose morphisms are magma homomorphisms (which are equivalent to homomorphisms in the sense of universal algebra).
Nerve (category theory)
CONCEPT WITHIN MATHEMATICS
Nerve of a category; Classifying space (category theory); Classifying space of a category; Nerve functor; Nerve (mathematics)
In category theory, a discipline within mathematics, the nerve N(C) of a small category C is a simplicial set constructed from the objects and morphisms of C. The geometric realization of this simplicial set is a topological space, called the classifying space of the category C.
Theory of Categories
PHILOSOPHICAL CONCEPT
Ontological distinction; Ways of being; Relation (metaphysics); Category (philosophy); Categories of being; Ontological scheme; Categories (philosophy); Ontological category; Ontological categories; Ontological catalogue; Category of being; Theory of Categories
In ontology, the theory of categories concerns itself with the categories of being: the highest genera or kinds of entities. To investigate the categories of being, or simply categories, is to determine the most fundamental and the broadest classes of entities.
Monoidal category
CATEGORY ADMITTING TENSOR PRODUCTS
Tensor category; Lax monoidal category; Monoidal categories; Identity object; Unit object; Free strict monoidal category; Internal product; Unitor; Strict monoidal category; Category of endofunctors; Monoidal category of endofunctors
In mathematics, a monoidal category (or tensor category) is a category \mathbf C equipped with a bifunctor
Cyclic category
In mathematics, the cyclic category or cycle category or category of cycles is a category of finite cyclically ordered sets and degree-1 maps between them. It was introduced by .
Pseudo-abelian category
PREADDITIVE CATEGORY SUCH THAT EVERY IDEMPOTENT HAS A KERNEL
Pseudoabelian category; Karoubian 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
Category mistake
SEMANTIC OR ONTOLOGICAL ERROR
Category error; Category-mistake; Miscategorization
A category mistake, or category error, or categorical mistake, or mistake of category, is a semantic or ontological error in which things belonging to a particular category are presented as if they belong to a different category, or, alternatively, a property is ascribed to a thing that could not possibly have that property. An example is a person learning that the game of cricket involves team spirit, and after being given a demonstration of each player's role, asking which player performs the "team spirit".
Product (category theory)
GENERALIZED OBJECT IN CATEGORY THEORY
Categorical product; Product category theory; Category product
In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the Cartesian product of sets, the direct product of groups or rings, and the product of topological spaces. Essentially, the product of a family of objects is the "most general" object which admits a morphism to each of the given objects.
