## Category theory |

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## Basic concepts

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**Category theory**^{[1]} formalizes * category*, whose nodes are called

Several terms used in category theory, including the term "morphism", are used differently from their uses in the rest of mathematics. In category theory, morphisms obey conditions specific to category theory itself.

Category theory has practical applications in

- basic concepts
- applications of categories
- utility
- categories, objects, and morphisms
- functors
- natural transformations
- other concepts
- historical notes
- see also
- notes
- references
- further reading
- external links

Categories represent abstractions of other mathematical concepts.
Many areas of mathematics can be formalised by category theory as ^{[2]}

A basic example of a category is the

The "arrows" of category theory are often said to represent a process connecting two objects, or in many cases a "structure-preserving" transformation connecting two objects. There are, however, many applications where much more abstract concepts are represented by objects and morphisms. The most important property of the arrows is that they can be "composed", in other words, arranged in a sequence to form a new arrow.