Author : J. Lambek
Publisher : Cambridge University Press
Page : 308 pages
File Size : 37,40 MB
Release : 1988-03-25
Category : Mathematics
ISBN : 9780521356534
Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.
Author : B. Jacobs
Publisher : Gulf Professional Publishing
Page : 784 pages
File Size : 26,87 MB
Release : 2001-05-10
Category : Computers
ISBN : 9780444508539
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.
Author : M. Makkai
Publisher : Springer
Page : 317 pages
File Size : 17,47 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540371001
Author : Aldo Ursini
Publisher : Routledge
Page : 728 pages
File Size : 27,58 MB
Release : 2017-10-05
Category : Mathematics
ISBN : 1351434721
""Attempts to unite the fields of mathematical logic and general algebra. Presents a collection of refereed papers inspired by the International Conference on Logic and Algebra held in Siena, Italy, in honor of the late Italian mathematician Roberto Magari, a leading force in the blossoming of research in mathematical logic in Italy since the 1960s.
Author : Benjamin C. Pierce
Publisher : MIT Press
Page : 117 pages
File Size : 31,99 MB
Release : 1991-08-07
Category : Computers
ISBN : 0262326450
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
Author : Tom Leinster
Publisher : Cambridge University Press
Page : 193 pages
File Size : 33,52 MB
Release : 2014-07-24
Category : Mathematics
ISBN : 1107044243
A short introduction ideal for students learning category theory for the first time.
Author : Richard P. Stanley
Publisher : Cambridge University Press
Page : 641 pages
File Size : 26,23 MB
Release : 2012
Category : Mathematics
ISBN : 1107015421
Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation and differential posets.
Author : Edson de Faria
Publisher : Cambridge University Press
Page : 192 pages
File Size : 26,53 MB
Release : 2008-10-02
Category : Mathematics
ISBN : 1139474847
Originating with the pioneering works of P. Fatou and G. Julia, the subject of complex dynamics has seen great advances in recent years. Complex dynamical systems often exhibit rich, chaotic behavior, which yields attractive computer generated pictures, for example the Mandelbrot and Julia sets, which have done much to renew interest in the subject. This self-contained book discusses the major mathematical tools necessary for the study of complex dynamics at an advanced level. Complete proofs of some of the major tools are presented; some, such as the Bers-Royden theorem on holomorphic motions, appear for the very first time in book format. An appendix considers Riemann surfaces and Teichmüller theory. Detailing the very latest research, the book will appeal to graduate students and researchers working in dynamical systems and related fields. Carefully chosen exercises aid understanding and provide a glimpse of further developments in real and complex one-dimensional dynamics.
Author : Roy L. Crole
Publisher : Cambridge University Press
Page : 362 pages
File Size : 48,14 MB
Release : 1993
Category : Computers
ISBN : 9780521457019
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, natural transformations, the Yoneda lemma, cartesian closed categories, limits, adjunctions and indexed categories. Four kinds of formal system are considered in detail, namely algebraic, functional, polymorphic functional, and higher order polymorphic functional type theory. For each of these the categorical semantics are derived and results about the type systems are proved categorically. Issues of soundness and completeness are also considered. Aimed at advanced undergraduates and beginning graduates, this book will be of interest to theoretical computer scientists, logicians and mathematicians specializing in category theory.
Author : M. P. Brodmann
Publisher : Cambridge University Press
Page : 514 pages
File Size : 36,33 MB
Release : 2013
Category : Mathematics
ISBN : 0521513634
On its original publication, this algebraic introduction to Grothendieck's local cohomology theory was the first book devoted solely to the topic and it has since become the standard reference for graduate students. This second edition has been thoroughly revised and updated to incorporate recent developments in the field.
