Simplicial Methods for Operads and Algebraic Geometry - 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 Simplicial Methods for Operads and Algebraic Geometry write by Ieke Moerdijk. This book was released on 2010-12-01. Simplicial Methods for Operads and Algebraic Geometry available in PDF, EPUB and Kindle. "This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods. It is based on lectures delivered at the Centre de Recerca Matemàtica in February 2008, as part of a special year on Homotopy Theory and Higher Categories"--Foreword
Simplicial Methods for Higher Categories
Simplicial Methods for Higher 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 Simplicial Methods for Higher Categories write by Simona Paoli. This book was released on 2019-06-03. Simplicial Methods for Higher Categories available in PDF, EPUB and Kindle. This monograph presents a new model of mathematical structures called weak n-categories. These structures find their motivation in a wide range of fields, from algebraic topology to mathematical physics, algebraic geometry and mathematical logic. While strict n-categories are easily defined in terms associative and unital composition operations they are of limited use in applications, which often call for weakened variants of these laws. The author proposes a new approach to this weakening, whose generality arises not from a weakening of such laws but from the very geometric structure of its cells; a geometry dubbed weak globularity. The new model, called weakly globular n-fold categories, is one of the simplest known algebraic structures yielding a model of weak n-categories. The central result is the equivalence of this model to one of the existing models, due to Tamsamani and further studied by Simpson. This theory has intended applications to homotopy theory, mathematical physics and to long-standing open questions in category theory. As the theory is described in elementary terms and the book is largely self-contained, it is accessible to beginning graduate students and to mathematicians from a wide range of disciplines well beyond higher category theory. The new model makes a transparent connection between higher category theory and homotopy theory, rendering it particularly suitable for category theorists and algebraic topologists. Although the results are complex, readers are guided with an intuitive explanation before each concept is introduced, and with diagrams showing the interconnections between the main ideas and results.
Infinity Operads And Monoidal Categories With Group Equivariance
Infinity Operads And Monoidal Categories With Group Equivariance - 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 Infinity Operads And Monoidal Categories With Group Equivariance write by Donald Yau. This book was released on 2021-12-02. Infinity Operads And Monoidal Categories With Group Equivariance available in PDF, EPUB and Kindle. This monograph provides a coherent development of operads, infinity operads, and monoidal categories, equipped with equivariant structures encoded by an action operad. A group operad is a planar operad with an action operad equivariant structure. In the first three parts of this monograph, we establish a foundation for group operads and for their higher coherent analogues called infinity group operads. Examples include planar, symmetric, braided, ribbon, and cactus operads, and their infinity analogues. For example, with the tools developed here, we observe that the coherent ribbon nerve of the universal cover of the framed little 2-disc operad is an infinity ribbon operad.In Part 4 we define general monoidal categories equipped with an action operad equivariant structure and provide a unifying treatment of coherence and strictification for them. Examples of such monoidal categories include symmetric, braided, ribbon, and coboundary monoidal categories, which naturally arise in the representation theory of quantum groups and of coboundary Hopf algebras and in the theory of crystals of finite dimensional complex reductive Lie algebras.
Infinity Properads and Infinity Wheeled Properads
Infinity Properads and Infinity Wheeled Properads - 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 Infinity Properads and Infinity Wheeled Properads write by Philip Hackney. This book was released on 2015-09-07. Infinity Properads and Infinity Wheeled Properads available in PDF, EPUB and Kindle. The topic of this book sits at the interface of the theory of higher categories (in the guise of (∞,1)-categories) and the theory of properads. Properads are devices more general than operads and enable one to encode bialgebraic, rather than just (co)algebraic, structures. The text extends both the Joyal-Lurie approach to higher categories and the Cisinski-Moerdijk-Weiss approach to higher operads, and provides a foundation for a broad study of the homotopy theory of properads. This work also serves as a complete guide to the generalised graphs which are pervasive in the study of operads and properads. A preliminary list of potential applications and extensions comprises the final chapter. Infinity Properads and Infinity Wheeled Properads is written for mathematicians in the fields of topology, algebra, category theory, and related areas. It is written roughly at the second year graduate level, and assumes a basic knowledge of category theory.
A Handbook of Model Categories
A Handbook of Model 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 A Handbook of Model Categories write by Scott Balchin. This book was released on 2021-10-29. A Handbook of Model Categories available in PDF, EPUB and Kindle. This book outlines a vast array of techniques and methods regarding model categories, without focussing on the intricacies of the proofs. Quillen model categories are a fundamental tool for the understanding of homotopy theory. While many introductions to model categories fall back on the same handful of canonical examples, the present book highlights a large, self-contained collection of other examples which appear throughout the literature. In particular, it collects a highly scattered literature into a single volume. The book is aimed at anyone who uses, or is interested in using, model categories to study homotopy theory. It is written in such a way that it can be used as a reference guide for those who are already experts in the field. However, it can also be used as an introduction to the theory for novices.
