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Category Theory for Programming

2 Sep 2022arXiv:2209.01259links table onlyarchive 2025-07-28

Benedikt Ahrens, Kobe Wullaert

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In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical characterization of datatypes and recursive functions on them. Secondly, we study monads, which give a mathematical framework for effects in functional languages. The notes include many problems and solutions.

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