Definitions for category theory
cat·e·go·ry the·o·ry

WiktionaryRate this definition:0.0 / 0 votes

1. category theorynoun

   A branch of mathematics which deals with spaces and maps between them in abstraction, taking similar theorems from various disparate more concrete branches of mathematics and unifying them.

WikipediaRate this definition:0.0 / 0 votes

1. Category theory

   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. In particular, many constructions of new mathematical objects from previous ones, that appear similarly in several contexts are conveniently expressed and unified in terms of categories. Examples include quotient spaces, direct products, completion, and duality. A category is formed by two sorts of objects: the objects of the category, and the morphisms, which relate two objects called the source and the target of the morphism. One often says that a morphism is an arrow that maps its source to its target. Morphisms can be composed if the target of the first morphism equals the source of the second one, and morphism composition has similar properties as function composition (associativity and existence of identity morphisms). Morphisms are often some sort of function, but this is not always the case. For example, a monoid may be viewed as a category with a single object, whose morphisms are the elements of the monoid. The second fundamental concept of category is the concept of a functor, which plays the role of a morphism between two categories C 1 {\displaystyle C_{1}} and C 2 : {\displaystyle C_{2}:} it maps objects of C 1 {\displaystyle C_{1}} to objects of C 2 {\displaystyle C_{2}} and morphisms of C 1 {\displaystyle C_{1}} to morphisms of C 2 {\displaystyle C_{2}} in such a way that sources are mapped to sources and targets are mapped to targets (or, in the case of a contravariant functor, sources are mapped to targets and vice-versa). A third fundamental concept is a natural transformation that may be viewed as a morphism of functors.

WikidataRate this definition:0.0 / 0 votes

1. Category theory

   Category theory is used to formalize mathematics and its concepts as a collection of objects and arrows. Category theory can be used to formalize concepts of other high-level abstractions such as set theory, field theory, and group theory. Several terms used in category theory, including the term "morphism", differ from their uses within mathematics itself. In category theory, a "morphism" obeys a set of conditions specific to category theory itself. Thus, care must be taken to understand the context in which statements are made.

How to pronounce category theory?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say category theory in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of category theory in Chaldean Numerology is: 5

2. Pythagorean Numerology

   The numerical value of category theory in Pythagorean Numerology is: 5

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Category_Theory
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Category_Theory
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=category theory