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.
Homotopy Theory of Higher Categories
Homotopy Theory of 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 Homotopy Theory of Higher Categories write by Carlos Simpson. This book was released on 2011-10-20. Homotopy Theory of Higher Categories available in PDF, EPUB and Kindle. The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher categories. Starting with a cohesive overview of the many different approaches currently used by researchers, the author proceeds with a detailed exposition of one of the most widely used techniques: the construction of a Cartesian Quillen model structure for higher categories. The fully iterative construction applies to enrichment over any Cartesian model category, and yields model categories for weakly associative n-categories and Segal n-categories. A corollary is the construction of higher functor categories which fit together to form the (n+1)-category of n-categories. The approach uses Tamsamani's definition based on Segal's ideas, iterated as in Pelissier's thesis using modern techniques due to Barwick, Bergner, Lurie and others.
The $K$-book
The $K$-book - 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 The $K$-book write by Charles A. Weibel. This book was released on 2013-06-13. The $K$-book available in PDF, EPUB and Kindle. Informally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vector spaces and producing important intrinsic invariants which are useful in the study of algebr
