Elements Of Category Theory
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Elements Of Category Theory
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Author : Emily Riehl
language : en
Publisher: Cambridge University Press
Release Date : 2022-02-10
Elements Of Category Theory written by Emily Riehl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-10 with Mathematics categories.
This book develops the theory of infinite-dimensional categories by studying the universe, or ∞-cosmos, in which they live.
Higher Category Theory
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Author : Ezra Getzler
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Higher Category Theory written by Ezra Getzler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
Comprises six presentations on new developments in category theory from the March 1997 workshop. The topics are categorification, computads for finitary monads on globular sets, braided n- categories and a-structures, categories of vector bundles and Yang- Mills equations, the role of Michael Batanin's monoidal globular categories, and braided deformations of monoidal categories and Vassiliev invariants. No index. Annotation copyrighted by Book News, Inc., Portland, OR.
What Is Category Theory
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Author : Giandomenico Sica
language : en
Publisher: Polimetrica s.a.s.
Release Date : 2006
What Is Category Theory written by Giandomenico Sica and has been published by Polimetrica s.a.s. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Category Theory In Context
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Author : Emily Riehl
language : en
Publisher: Courier Dover Publications
Release Date : 2017-03-09
Category Theory In Context written by Emily Riehl and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-09 with Mathematics categories.
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.
Category Theory
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Author : Zoran Majkic
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-03-06
Category Theory written by Zoran Majkic and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-06 with Computers categories.
This book analyzes the generation of the arrow-categories of a given category, which is a foundational and distinguishable Category Theory phenomena, in analogy to the foundational role of sets in the traditional set-based Mathematics, for defi nition of natural numbers as well. This inductive transformation of a category into the infinite hierarchy of the arrowcategories is extended to the functors and natural transformations. The author considers invariant categorial properties (the symmetries) under such inductive transformations. The book focuses in particular on Global symmetry (invariance of adjunctions) and Internal symmetries between arrows and objects in a category (in analogy to Field Theories like Quantum Mechanics and General Relativity). The second part of the book is dedicated to more advanced applications of Internal symmetry to Computer Science: for Intuitionistic Logic, Untyped Lambda Calculus with Fixpoint Operators, Labeled Transition Systems in Process Algebras and Modal logics as well as Data Integration Theory.
Axiomatic Method And Category Theory
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Author : Andrei Rodin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-14
Axiomatic Method And Category Theory written by Andrei Rodin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-14 with Philosophy categories.
This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method.
Category Theory In Context
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Author : Emily Riehl
language : en
Publisher: Courier Dover Publications
Release Date : 2016-11-16
Category Theory In Context written by Emily Riehl and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-16 with Mathematics categories.
Category theory has provided the foundations for many of the twentieth century's greatest advances in pure mathematics. This concise, original text for a one-semester course on the subject is derived from courses that author Emily Riehl taught at Harvard and Johns Hopkins Universities. The treatment introduces the essential concepts of category theory: categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads, and other topics. Suitable for advanced undergraduates and graduate students in mathematics, the text provides tools for understanding and attacking difficult problems in algebra, number theory, algebraic geometry, and algebraic topology. Drawing upon a broad range of mathematical examples from the categorical perspective, the author illustrates how the concepts and constructions of category theory arise from and illuminate more basic mathematical ideas. Prerequisites are limited to familiarity with some basic set theory and logic.
Monoidal Category Theory
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Author : Noson S. Yanofsky
language : en
Publisher: MIT Press
Release Date : 2024-11-05
Monoidal Category Theory written by Noson S. Yanofsky and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-05 with Computers categories.
A comprehensive, cutting-edge, and highly readable textbook that makes category theory and monoidal category theory accessible to students across the sciences. Category theory is a powerful framework that began in mathematics but has since expanded to encompass several areas of computing and science, with broad applications in many fields. In this comprehensive text, Noson Yanofsky makes category theory accessible to those without a background in advanced mathematics. Monoidal Category Theorydemonstrates the expansive uses of categories, and in particular monoidal categories, throughout the sciences. The textbook starts from the basics of category theory and progresses to cutting edge research. Each idea is defined in simple terms and then brought alive by many real-world examples before progressing to theorems and uncomplicated proofs. Richly guided exercises ground readers in concrete computation and application. The result is a highly readable and engaging textbook that will open the world of category theory to many. Makes category theory accessible to non-math majors Uses easy-to-understand language and emphasizes diagrams over equations Incremental, iterative approach eases students into advanced concepts A series of embedded mini-courses cover such popular topics as quantum computing, categorical logic, self-referential paradoxes, databases and scheduling, and knot theory Extensive exercises and examples demonstrate the broad range of applications of categorical structures Modular structure allows instructors to fit text to the needs of different courses Instructor resources include slides
An Invitation To Applied Category Theory
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Author : Brendan Fong
language : en
Publisher: Cambridge University Press
Release Date : 2019-07-18
An Invitation To Applied Category Theory written by Brendan Fong and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-18 with Computers categories.
Category theory reveals commonalities between structures of all sorts. This book shows its potential in science, engineering, and beyond.
Category Theory And Applications A Textbook For Beginners Second Edition
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Author : Marco Grandis
language : en
Publisher: World Scientific
Release Date : 2021-03-05
Category Theory And Applications A Textbook For Beginners Second Edition written by Marco Grandis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-05 with Mathematics categories.
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.