Tag Archives: functor,

Category Theory for the Sciences

FREEDownload : Category Theory for the Sciences

Category Theory for the Sciences by David I. Spivak
2014 | ISBN: 0262028131 | English | 496 pages | PDF | 7 MB

Category Theory for the Sciences
Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs — categories in disguise. After explaining the "big three" concepts of category theory — categories, functors, and natural transformations — the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with selected solutions. is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.
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Introduction to the Theory of Categories and Functions

I. Bucur, A. Deleanu, "Introduction to the Theory of Categories and Functions"
1968 | pages: 232 | ISBN: 047011651X | PDF | 13,3 mb
The theory of categories has arisen in the last twenty-five years and now constitutes an autonomous branch of mathematics. It owes its origin and early inspiration to developments in algebraic topology. When the basic concepts of category, functor, natural transformation and natural equivalence were first formulated by Eilenberg and MacLane they served immediately to provide the appropriate framework for describing the way in which algebraic tools were used, and could be used, in the study of topology. It was surely evident from the outset, to the inventors of these fundamental notions and to others, that their domain of application certainly extended far beyond that of algebraic topology. Indeed there were clearly many applications within algebra itself, and homological algebra began to emerge as a mathematical discipline in its own right concerned with abelian categories and their specializations to categories of modules. However, it was not clear in the early stages that there was a "pure" theory latent within the domain of categories and functors which was capable of assuming substantial proportions within the body of mathematics. Of course, the original basic concepts came to be reinforced by auxiliary notions suggested by applications of those concepts; and many arguments traditionally carried out in a more specialized setting were seen to fit naturally into the more abstract framework of category theory. Nevertheless, it is only in the last ten years, or less, that the source of inspiration for advances in category theory has come to any considerable extent from within the theory itself. Once this process had begun it accelerated rapidly, so that now the corpus of knowledge has increased enormously and with this advance has come a great increase in the scope of application of the theory, to include such widely scattered parts of mathematics as functional analysis and mathematical logic.

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