(Co)end Calculus - 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 (Co)end Calculus write by Fosco Loregian. This book was released on 2021-07-22. (Co)end Calculus available in PDF, EPUB and Kindle. This easy-to-cite handbook gives the first systematic treatment of the (co)end calculus in category theory and its applications.
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 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.
Basic Concepts of Enriched Category Theory
Basic Concepts of Enriched 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 Concepts of Enriched Category Theory write by Gregory Maxwell Kelly. This book was released on 1982-02-18. Basic Concepts of Enriched Category Theory available in PDF, EPUB and Kindle.
Categorical Homotopy Theory
Categorical Homotopy 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 Categorical Homotopy Theory write by Emily Riehl. This book was released on 2014-05-26. Categorical Homotopy Theory available in PDF, EPUB and Kindle. 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.
Tensor Categories
Tensor Categories - 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 Tensor Categories write by Pavel Etingof. This book was released on 2016-08-05. Tensor Categories available in PDF, EPUB and Kindle. Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
