Category Theory And Applications A Textbook For Beginners Second Edition
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Category Theory And Applications A Textbook For Beginners Second Edition
Author | : Marco Grandis |
Publsiher | : World Scientific |
Total Pages | : 390 |
Release | : 2021-03-05 |
Genre | : Mathematics |
ISBN | : 9789811236105 |
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Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a better understanding of their roots.This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers the basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications.A reader should have some elementary knowledge of these three subjects, or at least two of them, in order to be able to follow the main examples, appreciate the unifying power of the categorical approach, and discover the subterranean links brought to light and formalised by this perspective.Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications in Algebra and Topology, with a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.In this second edition, the book has been entirely reviewed, adding many applications and exercises. All non-obvious exercises have now a solution (or a reference, in the case of an advanced topic); solutions are now collected in the last chapter.
Category Theory and Applications
![Category Theory and Applications](https://youbookinc.com/wp-content/uploads/2024/06/cover.jpg)
Author | : Marco Grandis |
Publsiher | : Unknown |
Total Pages | : 294 |
Release | : 2018 |
Genre | : Categories (Mathematics) |
ISBN | : 9813231076 |
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Category Theory in Context
Author | : Emily Riehl |
Publsiher | : Courier Dover Publications |
Total Pages | : 272 |
Release | : 2017-03-09 |
Genre | : Mathematics |
ISBN | : 9780486820804 |
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Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.
Basic Category Theory
Author | : Tom Leinster |
Publsiher | : Cambridge University Press |
Total Pages | : 193 |
Release | : 2014-07-24 |
Genre | : Mathematics |
ISBN | : 9781107044241 |
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A short introduction ideal for students learning category theory for the first time.
Basic Category Theory for Computer Scientists
Author | : Benjamin C. Pierce |
Publsiher | : MIT Press |
Total Pages | : 117 |
Release | : 1991-08-07 |
Genre | : Computers |
ISBN | : 9780262326452 |
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Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Contents Tutorial • Applications • Further Reading
Categories for the Working Mathematician
Author | : Saunders Mac Lane |
Publsiher | : Springer Science & Business Media |
Total Pages | : 320 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 9781475747218 |
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An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.
An Invitation to Applied Category Theory
Author | : Brendan Fong,David I. Spivak |
Publsiher | : Cambridge University Press |
Total Pages | : 351 |
Release | : 2019-07-18 |
Genre | : Computers |
ISBN | : 9781108482295 |
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Category theory reveals commonalities between structures of all sorts. This book shows its potential in science, engineering, and beyond.
Algebraic Topology A Structural Introduction
Author | : Marco Grandis |
Publsiher | : World Scientific |
Total Pages | : 372 |
Release | : 2021-12-24 |
Genre | : Mathematics |
ISBN | : 9789811248375 |
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Algebraic Topology is a system and strategy of partial translations, aiming to reduce difficult topological problems to algebraic facts that can be more easily solved. The main subject of this book is singular homology, the simplest of these translations. Studying this theory and its applications, we also investigate its underlying structural layout - the topics of Homological Algebra, Homotopy Theory and Category Theory which occur in its foundation.This book is an introduction to a complex domain, with references to its advanced parts and ramifications. It is written with a moderate amount of prerequisites — basic general topology and little else — and a moderate progression starting from a very elementary beginning. A consistent part of the exposition is organised in the form of exercises, with suitable hints and solutions.It can be used as a textbook for a semester course or self-study, and a guidebook for further study.