Categories for the Working Mathematician - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Categories for the Working Mathematician write by Saunders Mac Lane. This book was released on 2013-04-17. Categories for the Working Mathematician available in PDF, EPUB and Kindle. An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.
Categories for the Working Mathematician
Categories for the Working Mathematician - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Categories for the Working Mathematician write by Saunders MacLane. This book was released on 2013-11-11. Categories for the Working Mathematician available in PDF, EPUB and Kindle. Category Theory has developed rapidly. This book aims to present those ideas and methods which can now be effectively used by Mathe maticians working in a variety of other fields of Mathematical research. This occurs at several levels. On the first level, categories provide a convenient conceptual language, based on the notions of category, functor, natural transformation, contravariance, and functor category. These notions are presented, with appropriate examples, in Chapters I and II. Next comes the fundamental idea of an adjoint pair of functors. This appears in many substantially equivalent forms: That of universal construction, that of direct and inverse limit, and that of pairs offunctors with a natural isomorphism between corresponding sets of arrows. All these forms, with their interrelations, are examined in Chapters III to V. The slogan is "Adjoint functors arise everywhere". Alternatively, the fundamental notion of category theory is that of a monoid -a set with a binary operation of multiplication which is associative and which has a unit; a category itself can be regarded as a sort of general ized monoid. Chapters VI and VII explore this notion and its generaliza tions. Its close connection to pairs of adjoint functors illuminates the ideas of universal algebra and culminates in Beck's theorem characterizing categories of algebras; on the other hand, categories with a monoidal structure (given by a tensor product) lead inter alia to the study of more convenient categories of topological spaces.
Categories for the Working Philosopher
Categories for the Working Philosopher - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Categories for the Working Philosopher write by Elaine M. Landry. This book was released on 2017. Categories for the Working Philosopher available in PDF, EPUB and Kindle. This is the first volume on category theory for a broad philosophical readership. It is designed to show the interest and significance of category theory for a range of philosophical interests: mathematics, proof theory, computation, cognition, scientific modelling, physics, ontology, the structure of the world. Each chapter is written by either a category-theorist or a philosopher working in one of the represented areas, in an accessible waythat builds on the concepts that are already familiar to philosophers working in these areas.
Basic Category Theory
Basic Category Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Basic Category Theory write by Tom Leinster. This book was released on 2014-07-24. Basic Category Theory available in PDF, EPUB and Kindle. A short introduction ideal for students learning category theory for the first time.
Category Theory in Context
Category Theory in Context - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Category Theory in Context write by Emily Riehl. This book was released on 2017-03-09. Category Theory in Context available in PDF, EPUB and Kindle. 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.
