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Cover: 9781108711821 | An Invitation to Applied Category Theory | Brendan Fong (u. a.) | Buch
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An Invitation to Applied Category Theory
Seven Sketches in Compositionality
Taschenbuch von Brendan Fong (u. a.)
Sprache: Englisch

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Beschreibung
Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics.
Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics.
Über den Autor
Brendan Fong is a postdoctoral associate in the Department of Mathematics at the Massachusetts Institute of Technology. His research explores how we use pictures to represent and reason about the systems around us, and how to understand the world from a relational point of view. These topics find their intersection in applied category theory.
Inhaltsverzeichnis
Preface; 1. Generative effects: orders and Galois connections; 2. Resource theories: monoidal preorders and enrichment; 3. Databases: categories, functors, and universal constructions; 4. Collaborative design: profunctors, categorification, and monoidal categories; 5. Signal flow graphs: props, presentations, and proofs; 6. Electric circuits: hypergraph categories and operads; 7. Logic of behavior: sheaves, toposes, and internal languages; Appendix. Exercise solutions; References; Index.
Details
Erscheinungsjahr: 2019
Fachbereich: Grundlagen
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: Kartoniert / Broschiert
ISBN-13: 9781108711821
ISBN-10: 1108711820
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Fong, Brendan
Spivak, David I
Hersteller: Cambridge University Press
Verantwortliche Person für die EU: Produktsicherheitsverantwortliche/r, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße: 246 x 175 x 22 mm
Von/Mit: Brendan Fong (u. a.)
Erscheinungsdatum: 29.08.2019
Gewicht: 0,686 kg
Artikel-ID: 115388212
Über den Autor
Brendan Fong is a postdoctoral associate in the Department of Mathematics at the Massachusetts Institute of Technology. His research explores how we use pictures to represent and reason about the systems around us, and how to understand the world from a relational point of view. These topics find their intersection in applied category theory.
Inhaltsverzeichnis
Preface; 1. Generative effects: orders and Galois connections; 2. Resource theories: monoidal preorders and enrichment; 3. Databases: categories, functors, and universal constructions; 4. Collaborative design: profunctors, categorification, and monoidal categories; 5. Signal flow graphs: props, presentations, and proofs; 6. Electric circuits: hypergraph categories and operads; 7. Logic of behavior: sheaves, toposes, and internal languages; Appendix. Exercise solutions; References; Index.
Details
Erscheinungsjahr: 2019
Fachbereich: Grundlagen
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: Kartoniert / Broschiert
ISBN-13: 9781108711821
ISBN-10: 1108711820
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Fong, Brendan
Spivak, David I
Hersteller: Cambridge University Press
Verantwortliche Person für die EU: Produktsicherheitsverantwortliche/r, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße: 246 x 175 x 22 mm
Von/Mit: Brendan Fong (u. a.)
Erscheinungsdatum: 29.08.2019
Gewicht: 0,686 kg
Artikel-ID: 115388212
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