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Category theory using Haskellan introduction with Moggi and Yoneda /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Category theory using Haskellby Shuichi Yukita.
Reminder of title:	an introduction with Moggi and Yoneda /
Author:	Yukita, Shuichi.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xi, 297 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Categories (Mathematics)
Online resource:	https://doi.org/10.1007/978-3-031-68538-5
ISBN:	9783031685385$q(electronic bk.)

Category theory using Haskellan introduction with Moggi and Yoneda /
Yukita, Shuichi.

Category theory using Haskellan introduction with Moggi and Yoneda /[electronic resource] :by Shuichi Yukita. - Cham :Springer Nature Switzerland :2025. - xi, 297 p. :ill. (some col.), digital ;24 cm. - Computer science foundations and applied logic,2731-5762. - Computer science foundations and applied logic..

1. Catetory, Functor, Natural Transformation -- 2. Equivalence of categories -- 3. Universality and Limits -- 4. Functors and Limits -- 5. Adjoints -- 6. Monads -- 7. Representable Functors.

This unique book offers an introductory course on category theory, which became a working language in algebraic geometry and number theory in the 1950s and began to spread to logic and computer science soon after it was created. Offering excellent use of helpful examples in Haskell, the work covers (among other things) concepts of functors, natural transformations, monads, adjoints, universality, category equivalence, and many others. The main goal is to understand the Yoneda lemma, which can be used to reverse-engineer the implementation of a function. Later chapters offer more insights into computer science, including computation with output, nondeterministic computation, and continuation passing. Topics and features: Contains rigorous mathematical arguments to support the theory Provides numerous Haskell code-implementing examples Engages with plentiful diagram chasing, with special emphasis on the design patterns for constructing a large diagram out of basic small pieces Offers insights into category theory to quantum computing and the foundation of computing discipline Serves as a preparatory course for monoidal categories and higher categories The work will be useful to undergraduate students in computer science who have enough background in college mathematics such as linear algebra and basics in Haskell polymorphic functions. Further, it will appeal to graduate students and researchers in computing disciplines who want to newly acquire serious knowledge of category theory. Prof. Shuichi Yukita is with the Faculty of Computer and Information Sciences at Hosei University, Hosei, Japan.

ISBN: 9783031685385$q(electronic bk.)

Standard No.: 10.1007/978-3-031-68538-5doiSubjects--Topical Terms:

206297
Categories (Mathematics)

LC Class. No.: QA76.9.M35 / Y85 2025

Dewey Class. No.: 004.0151

Category theory using Haskellan introduction with Moggi and Yoneda /
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520 $a This unique book offers an introductory course on category theory, which became a working language in algebraic geometry and number theory in the 1950s and began to spread to logic and computer science soon after it was created. Offering excellent use of helpful examples in Haskell, the work covers (among other things) concepts of functors, natural transformations, monads, adjoints, universality, category equivalence, and many others. The main goal is to understand the Yoneda lemma, which can be used to reverse-engineer the implementation of a function. Later chapters offer more insights into computer science, including computation with output, nondeterministic computation, and continuation passing. Topics and features: Contains rigorous mathematical arguments to support the theory Provides numerous Haskell code-implementing examples Engages with plentiful diagram chasing, with special emphasis on the design patterns for constructing a large diagram out of basic small pieces Offers insights into category theory to quantum computing and the foundation of computing discipline Serves as a preparatory course for monoidal categories and higher categories The work will be useful to undergraduate students in computer science who have enough background in college mathematics such as linear algebra and basics in Haskell polymorphic functions. Further, it will appeal to graduate students and researchers in computing disciplines who want to newly acquire serious knowledge of category theory. Prof. Shuichi Yukita is with the Faculty of Computer and Information Sciences at Hosei University, Hosei, Japan.
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