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Category theory formalizes mathematical structure and its concepts in terms of a collection of objects and of arrows (also called morphisms). A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. The language of category theory has been used to formalize concepts of other high-level abstractions such as sets, rings, and groups. 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. Samuel Eilenberg and Saunders Mac Lane introduced the concepts of categories, functors, and natural transformations in 1942–45 in their study of algebraic topology, with the goal of understanding the processes that preserve mathematical structure. Category theory has practical applications in programming language theory, in particular for the study of monads in functional programming.

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Hiragana

ひらがな

The rounded, flowing kana. Hiragana writes native Japanese words, grammar endings, and anything without (or alongside) kanji — it's the first script you learn. Each character stands for one syllable.

Example

ねこ — cat