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Categories for the Working Mathematician
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Saunders MacLane
"Categories for the Working Mathematician" provides 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. The book then turns to adjoint functors, which provide a description of universal constructions, an analysis ...
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Mathematical Methods: For Students of Physics and Related Fields
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Sadri Hassani
Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important ...
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Categories and Computer Science
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R F C Walters
Category theory has become increasingly important and popular in computer science, and many universities now have introductions to category theory as part of their courses for undergraduate computer scientists. The author is a respected category theorist and has based this textbook on a course given over the last few years at the University of ...
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Theory of Mathematical Structures
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Jiri Adamek
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Categorical Perspectives
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Jrgen Koslowski (Editor), Ja1/4rgen Koslowski (Editor), Jurgen Koslowski
This book consists of introductory surveys as well as articles containing original research and complete proofs devoted mainly to the theoretical and foundational developments of category theory and its applications to other fields. A number of articles in the areas of topology, algebra and computer science reflect the varied interests of George ...
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Topology and Category Theory in Computer Science
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G M Reed (Editor), R F Wachter (Editor), A W Roscoe (Editor)
The Oxford Topology Symposium was held in June 1989. Since techniques from topology and category theory have been used increasingly by theoretical computer scientists in recent years, it was decided to hold a special session at the symposium which would be devoted to the application of these topics in computer science. By holding this session in ...
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Categories for types
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by
Crole
This textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories. It introduces the reader to ordered set theory, lattices and domains, and this material provides plenty of examples for an introduction to category theory. which covers categories, functors, ...
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Conceptual Mathematics: A First Introduction to Categories
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F William Lawvere, Stephen H Schanuel
In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics introduces this tool for the learning, development, and use of mathematics, to beginning students and also to practising mathematical scientists. This book provides a skeleton key that makes explicit ...
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Structured Ring Spectra
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Andrew Baker (Editor), Birgit Richter (Editor), J W S Cassels (Editor)
Within algebraic topology, the prominent role of multiplicative cohomology theories has led to a great deal of foundational research on ring spectra and in the 1990s this gave rise to significant new approaches to constructing categories of spectra and ring-like objects in them. This book contains some important new contributions to the theory of ...
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Categorical Closure Operators
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by
Gabriele Castellini
This book presents the general theory of categorical closure operators together with examples and applications to the most common categories, such as topological spaces, fuzzy topological spaces, groups, and abelian groups. The main aim of the theory is to develop a categorical characterization of the classical basic concepts in topology via the ...
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Measure and Category: A Survey of the Analogies Between Topological and Measure Spaces
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John C Oxtoby
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Algebraic Homotopy
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Hans Joachim Baues
This book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed from a few axioms and are thus available in a broad variety of contexts. Many examples and applications in topology and algebra are discussed, including an introduction to rational homotopy theory in terms of ...
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Applications of Categories in Computer Science: Proceedings of the London Mathematical Society Symposium, Durham 1991
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M P Fourman, P T Johnstone (Editor), A M Pitts (Editor)
Category theory and related topics of mathematics have been increasingly applied to computer science in recent years. This book contains selected papers from the London Mathematical Society Symposium on the subject which was held at the University of Durham. Participants at the conference were leading computer scientists and mathematicians working ...
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Sets, Logic and Categories
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by
Peter J Cameron
Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Godel's Theorem, and the Skolem Paradox. But they are also rich mathematical theories in their own right, contributing techniques and results to working mathematicians such as the ...
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Locally Presentable and Accessible Categories
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Adámek, Rosický
The concepts of a locally presentable category and an accessible category have turned out to be useful in formulating connections between universal algebra, model theory, logic and computer science. The aim of this book is to provide an exposition of both the theory and the applications of these categories at a level accessible to graduate ...
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FPF ring theory faithful modules and generators of mod-R
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Faith, Page
This is the first book on the subject of FPF rings and the systematic use of the notion of the generator of the category mod-R of all right R-modules and its relationship to faithful modules. This carries out the program, explicit of inherent, in the work of G Azumaya, H. Bass, R. Dedekind, S. Endo, I. Kaplansky, K. Morita, T. Nakayama, R. Thrall, ...
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Handbook of Categorical Algebra: Volume 2, Categories and Structures
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by
Francis Borceux
The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence. The second, which assumes familiarity with the material in the first, introduces important classes of ...
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The duality of compact semigroups and C*-bigebras
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Karl H Hofmann
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Fundamentals of Algebraic Graph Transformation
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Hartmut Ehrig, Karsten Ehrig, Ulrike Prange
Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on ...
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Triangulated Categories. (Am-148)
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by
Amnon Neeman
The first two chapters of this book offer a modern, self-contained exposition of the elementary theory of triangulated categories and their quotients. The simple, elegant presentation of these known results makes these chapters eminently suitable as a text for graduate students. The remainder of the book is devoted to new research, providing, ...
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Triangulated Categories in the Representation of Finite Dimensional Algebras
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Dieter Happel, J W S Cassels (Editor), N J Hitchin (Editor)
This book is an introduction to the use of triangulated categories in the study of representations of finite-dimensional algebras. In recent years representation theory has been an area of intense research and the author shows that derived categories of finite-dimensional algebras are a useful tool in studying tilting processes. Results on the ...
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Introduction to Categories, Homological Algebra and Sheaf Cohomology
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Jan R Strooker
Categories, homological algebra, sheaves and their cohomology furnish useful methods for attacking problems in a variety of mathematical fields. This textbook provides an introduction to these methods, describing their elements and illustrating them by examples.
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Hausdorff Spectra in Functional Analysis
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by
Eugeny Smirnov, I Tweddle (Translator)
Self-contained, and collating for the first time material that has until now only been published in journals - often in Russian - this book will be of interest to functional analysts, especially those with interests in topological vector spaces, and to algebraists concerned with category theory. The closed graph theorem is one of the corner stones ...
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Applications of Category Theory to Fuzzy Subsets
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by
Rodabaugh, Klement, Höhle
"Applications of Category Theory to Fuzzy Subsets" is the first major work to comprehensively describe the deeper mathematical aspects of fuzzy sets, particularly those aspects which are category-theoretic in nature, and is intimately related to the first eleven years of the renowned International Seminar on Fuzzy Set Theory. Though it brings the ...
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Kan extensions in enriched category theory
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Eduardo J. Dubuc
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