Higher Segal Spaces - 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 Higher Segal Spaces write by Tobias Dyckerhoff. This book was released on 2019-10-17. Higher Segal Spaces available in PDF, EPUB and Kindle. This monograph initiates a theory of new categorical structures that generalize the simplicial Segal property to higher dimensions. The authors introduce the notion of a d-Segal space, which is a simplicial space satisfying locality conditions related to triangulations of d-dimensional cyclic polytopes. Focus here is on the 2-dimensional case. Many important constructions are shown to exhibit the 2-Segal property, including Waldhausen’s S-construction, Hecke-Waldhausen constructions, and configuration spaces of flags. The relevance of 2-Segal spaces in the study of Hall and Hecke algebras is discussed. Higher Segal Spaces marks the beginning of a program to systematically study d-Segal spaces in all dimensions d. The elementary formulation of 2-Segal spaces in the opening chapters is accessible to readers with a basic background in homotopy theory. A chapter on Bousfield localizations provides a transition to the general theory, formulated in terms of combinatorial model categories, that features in the main part of the book. Numerous examples throughout assist readers entering this exciting field to move toward active research; established researchers in the area will appreciate this work as a reference.
On the Theory of Higher Segal Spaces
On the Theory of Higher Segal Spaces - 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 On the Theory of Higher Segal Spaces write by Tashi Walde. This book was released on 2020. On the Theory of Higher Segal Spaces available in PDF, EPUB and Kindle.
Higher Topos Theory
Higher Topos 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 Higher Topos Theory write by Jacob Lurie. This book was released on 2009-07-26. Higher Topos Theory available in PDF, EPUB and Kindle. In 'Higher Topos Theory', Jacob Lurie presents the foundations of this theory using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.
Towards Higher Categories
Towards 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 Towards Higher Categories write by John C. Baez. This book was released on 2009-09-24. Towards Higher Categories available in PDF, EPUB and Kindle. The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory itself. It begins with a paper by John Baez and Michael Shulman which explores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eyes of n-category theory. The idea is to give some of the motivations behind this subject. There are then two survey articles, by Julie Bergner and Simona Paoli, about (infinity,1) categories and about the algebraic modelling of homotopy n-types. These are areas that are particularly well understood, and where a fully integrated theory exists. The main focus of the book is on the richness to be found in the theory of bicategories, which gives the essential starting point towards the understanding of higher categorical structures. An article by Stephen Lack gives a thorough, but informal, guide to this theory. A paper by Larry Breen on the theory of gerbes shows how such categorical structures appear in differential geometry. This book is dedicated to Max Kelly, the founder of the Australian school of category theory, and an historical paper by Ross Street describes its development.
Goodwillie Approximations to Higher Categories
Goodwillie Approximations to 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 Goodwillie Approximations to Higher Categories write by Gijs Heuts. This book was released on 2021-11-16. Goodwillie Approximations to Higher Categories available in PDF, EPUB and Kindle. View the abstract.
