Indexed Categories and Their Applications
Author: P.I. Johnstone
Publisher: Springer
Published: 2006-11-15
Total Pages: 271
ISBN-13: 3540357629
DOWNLOAD EBOOKRead and Download eBook Full
Author: P.I. Johnstone
Publisher: Springer
Published: 2006-11-15
Total Pages: 271
ISBN-13: 3540357629
DOWNLOAD EBOOKAuthor: Andrew M. Bruckner
Publisher:
Published: 1978
Total Pages: 216
ISBN-13: 9780387089133
DOWNLOAD EBOOKAuthor: Gregory Maxwell Kelly
Publisher: CUP Archive
Published: 1982-02-18
Total Pages: 260
ISBN-13: 9780521287029
DOWNLOAD EBOOKAuthor: B. Jacobs
Publisher: Gulf Professional Publishing
Published: 2001-05-10
Total Pages: 784
ISBN-13: 9780444508539
DOWNLOAD EBOOKThis 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.
Author: Emily Riehl
Publisher: Courier Dover Publications
Published: 2017-03-09
Total Pages: 273
ISBN-13: 0486820807
DOWNLOAD EBOOKIntroduction 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.
Author: Peter T. Johnstone
Publisher:
Published: 1978
Total Pages: 260
ISBN-13:
DOWNLOAD EBOOKAuthor: Marco Grandis
Publisher: World Scientific
Published: 2018-01-16
Total Pages: 305
ISBN-13: 9813231084
DOWNLOAD EBOOKCategory 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 deeper 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 its 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.Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications and a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.
Author: K. W. Potter
Publisher:
Published: 1966
Total Pages: 180
ISBN-13:
DOWNLOAD EBOOKAuthor: Marc Bezem
Publisher: Springer Science & Business Media
Published: 1993-03-03
Total Pages: 452
ISBN-13: 9783540565178
DOWNLOAD EBOOKThe lambda calculus was developed in the 1930s by Alonzo Church. The calculus turned out to be an interesting model of computation and became theprototype for untyped functional programming languages. Operational and denotational semantics for the calculus served as examples for otherprogramming languages. In typed lambda calculi, lambda terms are classified according to their applicative behavior. In the 1960s it was discovered that the types of typed lambda calculi are in fact appearances of logical propositions. Thus there are two possible views of typed lambda calculi: - as models of computation, where terms are viewed as programs in a typed programming language; - as logical theories, where the types are viewed as propositions and the terms as proofs. The practical spin-off from these studies are: - functional programming languages which are mathematically more succinct than imperative programs; - systems for automated proof checking based on lambda caluli. This volume is the proceedings of TLCA '93, the first international conference on Typed Lambda Calculi and Applications,organized by the Department of Philosophy of Utrecht University. It includes29 papers selected from 51 submissions.
Author: Mihály Makkai
Publisher: American Mathematical Soc.
Published: 1989
Total Pages: 186
ISBN-13: 082185111X
DOWNLOAD EBOOKIntended for category theorists and logicians familiar with basic category theory, this book focuses on categorical model theory, which is concerned with the categories of models of infinitary first order theories, called accessible categories. The starting point is a characterization of accessible categories in terms of concepts familiar from Gabriel-Ulmer's theory of locally presentable categories. Most of the work centers on various constructions (such as weighted bilimits and lax colimits), which, when performed on accessible categories, yield new accessible categories. These constructions are necessarily 2-categorical in nature; the authors cover some aspects of 2-category theory, in addition to some basic model theory, and some set theory. One of the main tools used in this study is the theory of mixed sketches, which the authors specialize to give concrete results about model theory. Many examples illustrate the extent of applicability of these concepts. In particular, some applications to topos theory are given. Perhaps the book's most significant contribution is the way it sets model theory in categorical terms, opening the door for further work along these lines. Requiring a basic background in category theory, this book will provide readers with an understanding of model theory in categorical terms, familiarity with 2-categorical methods, and a useful tool for studying toposes and other categories.