Category Theory Applied to Computation and Control
Author : E.G. Manes
Publisher : Lecture Notes in Computer Science
Page : 270 pages
File Size : 27,18 MB
Release : 1975-02-25
Category : Computers
ISBN :
Category Theory for Computing Science
Author : Michael Barr
Publisher :
Page : 352 pages
File Size : 31,86 MB
Release : 1995
Category : Computers
ISBN :
Book Description
A wide coverage of topics in category theory and computer science is developed in this text, including introductory treatments of cartesian closed categories, sketches and elementary categorical model theory, and triples. Over 300 exercises are included.
An Invitation to Applied Category Theory
Author : Brendan Fong
Publisher : Cambridge University Press
Page : 351 pages
File Size : 12,60 MB
Release : 2019-07-18
Category : Mathematics
ISBN : 1108582249
Book Description
Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics.
Category Theory in Context
Author : Emily Riehl
Publisher : Courier Dover Publications
Page : 273 pages
File Size : 21,98 MB
Release : 2017-03-09
Category : Mathematics
ISBN : 0486820807
Book Description
Introduction 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.
Computational Category Theory
Author : David E. Rydeheard
Publisher :
Page : 280 pages
File Size : 15,25 MB
Release : 1988
Category : Mathematics
ISBN :
Book Description
Basic Category Theory for Computer Scientists
Author : Benjamin C. Pierce
Publisher : MIT Press
Page : 117 pages
File Size : 26,17 MB
Release : 1991-08-07
Category : Computers
ISBN : 0262326450
Book Description
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
Mathematical Control Theory
Author : Eduardo D. Sontag
Publisher : Springer Science & Business Media
Page : 543 pages
File Size : 44,47 MB
Release : 2013-11-21
Category : Mathematics
ISBN : 1461205778
Book Description
Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.
Categories, Types, and Structures
Author : Andrea Asperti
Publisher : MIT Press (MA)
Page : 330 pages
File Size : 33,60 MB
Release : 1991
Category : Computers
ISBN :
Book Description
Category theory is a mathematical subject whose importance in several areas of computer science, most notably the semantics of programming languages and the design of programmes using abstract data types, is widely acknowledged. This book introduces category theory at a level appropriate for computer scientists and provides practical examples in the context of programming language design.
Algebra, Topology, and Category Theory
Author : Alex Heller
Publisher : Academic Press
Page : 238 pages
File Size : 25,91 MB
Release : 2014-05-10
Category : Mathematics
ISBN : 1483262618
Book Description
Algebra, Topology, and Category Theory: A Collection of Papers in Honor of Samuel Eilenberg is a collection of papers dealing with algebra, topology, and category theory in honor of Samuel Eilenberg. Topics covered range from large modules over artin algebras to two-dimensional Poincaré duality groups, along with the homology of certain H-spaces as group ring objects. Variable quantities and variable structures in topoi are also discussed. Comprised of 16 chapters, this book begins by looking at the relationship between the representation theories of finitely generated and large (not finitely generated) modules over an artin algebra. The reader is then introduced to reduced bar constructions on deRham complexes; some properties of two-dimensional Poincaré duality groups; and properties invariant within equivalence types of categories. Subsequent chapters explore the work of Samuel Eilenberg in topology; local complexity of finite semigroups; global dimension of ore extensions; and the spectrum of a ringed topos. This monograph will be a useful resource for students and practitioners of algebra and mathematics.
Categorical Homotopy Theory
Author : Emily Riehl
Publisher : Cambridge University Press
Page : 371 pages
File Size : 16,53 MB
Release : 2014-05-26
Category : Mathematics
ISBN : 1139952633
Book Description
This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.
