Shuichi Yukita – författare

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 theoryProvides numerous Haskell code-implementing examplesEngages with plentiful diagram chasing, with special emphasis on the design patterns for constructing a large diagram out of basic small piecesOffers insights into category theory to quantum computing and the foundation of computing disciplineServes as a preparatory course for monoidal categories and higher categoriesThe 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.

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 theoryProvides numerous Haskell code-implementing examplesEngages with plentiful diagram chasing, with special emphasis on the design patterns for constructing a large diagram out of basic small piecesOffers insights into category theory to quantum computing and the foundation of computing disciplineServes 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.

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 theoryProvides numerous Haskell code-implementing examplesEngages with plentiful diagram chasing, with special emphasis on the design patterns for constructing a large diagram out of basic small piecesOffers insights into category theory to quantum computing and the foundation of computing disciplineServes as a preparatory course for monoidal categories and higher categoriesThe 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.

This book is designed as an undergraduate textbook for students in science and engineering, rather than for mathematics majors, yet it maintains full mathematical rigor. It covers groups, rings, modules over rings, finite fields, polynomial rings over finite fields, and error-correcting codes. Even in mathematics departments, undergraduates often wonder why concepts like normal subgroups and ideals matter, and standard textbooks may not provide satisfying answers. This book addresses such questions with both intuition and precision. For example: (1) A normal subgroup is the kernel of a group homomorphism and gives rise to a factor group; a non-normal subgroup does neither. (2) An ideal is a special additive subgroup that serves as the kernel of a ring homomorphism and yields a factor ring; a non-ideal additive subgroup does not. The reader will appreciate the elegant parallelism between these ideas. Key features include:A prerequisite chapter that subtly introduces module theory through an elementary presentation of the Euclidean algorithm, accessible even to high school students.Recurring use of orbits and clusters, with intuitive illustrations, to clarify the operational meaning of normal subgroups and ideals via homomorphisms.Emphasis on proof design patterns, inspired by fields like architecture and software engineering.Extensive use of diagrams to support conceptual understanding. Readers are encouraged to draw, compute, design reasoning flows, and then write proofs.Complete answers to quizzes and exercises are provided, allowing readers to check their understanding after thoughtful attempts.