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Sketches: Outline with references
, 1993
"... This package contains the original article, written in December, 1993, and this addendum, ..."
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This package contains the original article, written in December, 1993, and this addendum,
Scetches and Specifications User'S Gude  First . . .
, 2000
"... SKETCHES AND SPECIFICATIONS is a common denomination for several papers which deal with applications of Ehresmann’s sketch theory to computer science. These papers can be considered as the first steps towards a unified theory for software engineering. However, their aim is not to advocate a unificat ..."
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SKETCHES AND SPECIFICATIONS is a common denomination for several papers which deal with applications of Ehresmann’s sketch theory to computer science. These papers can be considered as the first steps towards a unified theory for software engineering. However, their aim is not to advocate a unification of computer languages; they are designed to build a frame for the study of notions which arise from several areas in computer science. These papers are arranged in two complementary families: REFERENCE MANUAL and USER’S GUIDE. The reference manual provides general definitions and results, with comprehensive proofs. On the other hand, the user’s guide places emphasis on motivations and gives a detailed description of several examples. These two families, though complementary, can be read independently. No prerequisite is assumed; however, it can prove helpful to be familiar either with specification techniques in computer science or with category theory in mathematics. These papers are under development, they are, or will be, available at:
ON CATEGORIES OF COHESIVE, ACTIVE SETS AND OTHER DYNAMIC SYSTEMS BY
"... This work is intended to contribute to a program of developing general concepts and methods for applying category theory to the modeling and solution o f scientic problems. It was motivated by my experiences as an engineering student studying continuum and kinetic models of
uid
ows. The language o ..."
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This work is intended to contribute to a program of developing general concepts and methods for applying category theory to the modeling and solution o f scientic problems. It was motivated by my experiences as an engineering student studying continuum and kinetic models of
uid
ows. The language of category theory is employed because it facilitates precise comparisons between diverse types of structures. Using this language to investigate relationships between
uid
ow models requires categorical specications of constitutive relations and of idioms occurring across classications of dynamic systems. It is shown that a categorytheoretic denition of chaotic system applies not only to the Smale horseshoe, a standard chaotic system, but also to Conway's \Game of Life " automaton. Symbolic dynamics of the \Dining Philosophers " relational system is computed. A category composed of stochastic matrices is dened and some of its elementary properties are developed. A categorical variant of symbolic dynamics is applied to a nite stochastic process. Using pointwise Kan extension formulas, conditions ensuring existence of certain representations among categories of dynamic systems are proved. iii For my parents iv Acknowledgments Thanks, Mom and Dad. You are the greatest. I am nally done! Thanks to my wife Susan for being supportive, generous, and trusting while I've worked on this and while we lived far apart. Thanks to my grandparents Byron Oliver, Wesley Wojtowicz, and Josephine Oliver. You are greatly missed. Aloha and thank you Janet Wojtowicz for the many things you still do for our family. Thanks Michele and Shane for the wellwishes.