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| Author | : J. Lambek |
| Publisher | : Cambridge University Press |
| Total Pages | : 308 |
| Release | : 1988-03-25 |
| Genre | : 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 |
| Total Pages | : 784 |
| Release | : 2001-05-10 |
| Genre | : 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 |
| Total Pages | : 317 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540371001 |
| Author | : Benjamin C. Pierce |
| Publisher | : MIT Press |
| Total Pages | : 117 |
| Release | : 1991-08-07 |
| Genre | : 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 |
| Total Pages | : 193 |
| Release | : 2014-07-24 |
| Genre | : Mathematics |
| ISBN | : 1107044243 |
A short introduction ideal for students learning category theory for the first time.
| Author | : Roy L. Crole |
| Publisher | : Cambridge University Press |
| Total Pages | : 362 |
| Release | : 1993 |
| Genre | : 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 | : R. M. Dudley |
| Publisher | : Cambridge University Press |
| Total Pages | : 452 |
| Release | : 1999-07-28 |
| Genre | : Mathematics |
| ISBN | : 0521461022 |
This treatise by an acknowledged expert includes several topics not found in any previous book.
| Author | : Maria Cristina Pedicchio |
| Publisher | : Cambridge University Press |
| Total Pages | : 452 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9780521834148 |
Publisher Description
| Author | : D. J. Benson |
| Publisher | : Cambridge University Press |
| Total Pages | : 296 |
| Release | : 1991-08-22 |
| Genre | : Mathematics |
| ISBN | : 9780521636520 |
A further introduction to modern developments in the representation theory of finite groups and associative algebras.
| Author | : Boris Zilber |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 132 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : 9780821897454 |
The 1970s saw the appearance and development in categoricity theory of a tendency to focus on the study and description of uncountably categorical theories in various special classes defined by natural algebraic or syntactic conditions. There have thus been studies of uncountably categorical theories of groups and rings, theories of a one-place function, universal theories of semigroups, quasivarieties categorical in infinite powers, and Horn theories. In Uncountably Categorical Theories , this research area is referred to as the special classification theory of categoricity. Zilber's goal is to develop a structural theory of categoricity, using methods and results of the special classification theory, and to construct on this basis a foundation for a general classification theory of categoricity, that is, a theory aimed at describing large classes of uncountably categorical structures not restricted by any syntactic or algebraic conditions.
