Book Description
This volume contains carefully selected and refereed paperspresented at the International Workshop on Categorical Topology,held at the University of L'Aquila, L'Aquila, Italy from August 31 toSeptember 4, 1994. This collection represents a wide range of current developments in thefield, and will be of interest to mathematicians whose work involvescategory theory. ... Read more

Book Description
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 newly introduced concept of categorical closure operators. This permits many topological ideas to be introduced in a topology-free environment and imported afterwards into a new category, which often yields interesting new insights into its structure.The first part of the book deals with the general theory, starting with basic definitions and gradually moving to more advanced properties. The second part includes applications to the classical concepts of epimorphisms, separation, compactness and connectedness. Every chapter ends with exercises. A comprehensive list of references for the reader who wants to consult original works and a good index complete the book."Categorical Closure Operators" is self-contained and can be considered as a graduate level text for topics courses in category theory, algebra, and topology. The book appeals mainly to graduate students and researchers in category theory and categorical topology, and to those interested in categorical methods applied to the most common concrete categories. The reader is expected to have some basic knowledge of algebra, topology and category theory; however, all recurrent categorical concepts are included in a preliminary chapter. ... Read more

Book Description
This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists. ... Read more

Customer Reviews (1)

Excellent book.
Excellent book. The best in its field. I would recommend it, particularly for students. ... Read more

Book Description

Goguen categories extend the relational calculus and its categorical formalization to the fuzzy world. Starting from the fundamental concepts of sets, binary relations and lattices this book introduces several categorical formulations of an abstract theory of relations such as allegories, Dedekind categories and related structures. It is shown that neither theory is sufficiently rich to describe basic operations on fuzzy relations. The book then introduces Goguen categories and provides a comprehensive study of these structures including their representation theory, and the definability of norm-based operations.

Book Description
This book provides a comprehensive categorical theory ofclosure operators, with applications to topological and uniformspaces, groups, R-modules, fields and topological groups, aswell as partially ordered sets and graphs. In particular, closureoperators are used to give solutions to the epimorphism andco-well-poweredness problem in many concrete categories.
The material is illustrated with many examples and exercises, and openproblems are formulated which should stimulate further research.
Audience: This volume will be of interest to graduate studentsand professional researchers in many branches of mathematics andtheoretical computer science. Knowledge of algebra, topology, and thebasic notions of category theory is assumed. ... Read more

Book Description
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 Strecker to whom this work is dedicated. Notable also are an exposition of the contributions and importance of George Strecker's research and a survey chapter on general category theory. ... Read more

Book Description
Aimed at starting researchers in the field, Realizability gives a rigorous, yet reasonable introduction to the basic concepts of a field which has passed several successive phases of abstraction. Material from previously unpublished sources such as Ph.D. theses, unpublished papers, etc. has been molded into one comprehensive presentation of the subject area.

- The first book to date on this subject area
- Provides an clear introduction to Realizability with a comprehensive bibliography
- Easy to read and mathematically rigorous
- Written by an expert in the field ... Read more