Grothendieck Construction of Bipermutative-Indexed 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 Grothendieck Construction of Bipermutative-Indexed Categories write by Donald Yau. This book was released on 2023-12-06. Grothendieck Construction of Bipermutative-Indexed Categories available in PDF, EPUB and Kindle. This monograph is the first and only book-length reference for this material. Contents of Chapter 2, Chapter 3, Part 2, and Part 3 is new, not having appeared in any of the research literature. The book will appeal to mathematicians interested in topology. Book shelved as a reference title.
Grothendieck Construction of Bipermutative-indexed Categories
Grothendieck Construction of Bipermutative-indexed 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 Grothendieck Construction of Bipermutative-indexed Categories write by Donald Ying Yau. This book was released on 2024. Grothendieck Construction of Bipermutative-indexed Categories available in PDF, EPUB and Kindle. "The Grothendieck construction provides an explicit link between indexed categories and opfibrations. It is a fundamental concept in category theory and related fields with far reaching applications. Bipermutative categories are categorifications of rings. They play a central role in algebraic K-theory and infinite loop space 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.
Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups
Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups - 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 Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups write by John Rognes. This book was released on 2008. Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups available in PDF, EPUB and Kindle. The author introduces the notion of a Galois extension of commutative $S$-algebras ($E_\infty$ ring spectra), often localized with respect to a fixed homology theory. There are numerous examples, including some involving Eilenberg-Mac Lane spectra of commutative rings, real and complex topological $K$-theory, Lubin-Tate spectra and cochain $S$-algebras. He establishes the main theorem of Galois theory in this generality. Its proof involves the notions of separable and etale extensions of commutative $S$-algebras, and the Goerss-Hopkins-Miller theory for $E_\infty$ mapping spaces. He shows that the global sphere spectrum $S$ is separably closed, using Minkowski's discriminant theorem, and he estimates the separable closure of its localization with respect to each of the Morava $K$-theories. He also defines Hopf-Galois extensions of commutative $S$-algebras and studies the complex cobordism spectrum $MU$ as a common integral model for all of the local Lubin-Tate Galois extensions. The author extends the duality theory for topological groups from the classical theory for compact Lie groups, via the topological study by J. R. Klein and the $p$-complete study for $p$-compact groups by T. Bauer, to a general duality theory for stably dualizable groups in the $E$-local stable homotopy category, for any spectrum $E$.
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.
