Goodwillie Approximations To Higher Categories
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Goodwillie Approximations To Higher Categories
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Author : Gijs Heuts
language : en
Publisher: American Mathematical Society
Release Date : 2021-11-16
Goodwillie Approximations To Higher Categories written by Gijs Heuts and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-16 with Mathematics categories.
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Goodwillie Approximations To Higher Categories
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Author : Gijsbert Heuts
language : en
Publisher:
Release Date : 2015
Goodwillie Approximations To Higher Categories written by Gijsbert Heuts and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
Goodwillie calculus involves the approximation of functors between higher categories by so-called polynomial functors. We show (under mild hypotheses) how to associate to a higher category C a Goodwillie tower, consisting of categories which are polynomial in an appropriate sense. These polynomial approximations enjoy universal properties with respect to polynomial functors out of C. Furthermore, we provide a classification of such Goodwillie towers in terms of the stabilization of C and the derivatives of the identity functor. In special cases this classification becomes very simple, allowing us to draw conclusions about the structure of the category C. As an example we give an application to Quillen's rational homotopy theory. In the sequel to this paper we work out consequences for the study of vn-periodic unstable homotopy theory and the Bousfield-Kuhn functors.
Handbook Of Homotopy Theory
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Author : Haynes Miller
language : en
Publisher: CRC Press
Release Date : 2020-01-23
Handbook Of Homotopy Theory written by Haynes Miller and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-23 with Mathematics categories.
The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.
Bousfield Classes And Ohkawa S Theorem
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Author : Takeo Ohsawa
language : en
Publisher: Springer Nature
Release Date : 2020-03-18
Bousfield Classes And Ohkawa S Theorem written by Takeo Ohsawa and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-18 with Mathematics categories.
This volume originated in the workshop held at Nagoya University, August 28–30, 2015, focusing on the surprising and mysterious Ohkawa's theorem: the Bousfield classes in the stable homotopy category SH form a set. An inspiring, extensive mathematical story can be narrated starting with Ohkawa's theorem, evolving naturally with a chain of motivational questions: Ohkawa's theorem states that the Bousfield classes of the stable homotopy category SH surprisingly forms a set, which is still very mysterious. Are there any toy models where analogous Bousfield classes form a set with a clear meaning? The fundamental theorem of Hopkins, Neeman, Thomason, and others states that the analogue of the Bousfield classes in the derived category of quasi-coherent sheaves Dqc(X) form a set with a clear algebro-geometric description. However, Hopkins was actually motivated not by Ohkawa's theorem but by his own theorem with Smith in the triangulated subcategory SHc, consisting of compact objects in SH. Now the following questions naturally occur: (1) Having theorems of Ohkawa and Hopkins-Smith in SH, are there analogues for the Morel-Voevodsky A1-stable homotopy category SH(k), which subsumes SH when k is a subfield of C?, (2) Was it not natural for Hopkins to have considered Dqc(X)c instead of Dqc(X)? However, whereas there is a conceptually simple algebro-geometrical interpretation Dqc(X)c = Dperf(X), it is its close relative Dbcoh(X) that traditionally, ever since Oka and Cartan, has been intensively studied because of its rich geometric and physical information. This book contains developments for the rest of the story and much more, including the chromatics homotopy theory, which the Hopkins–Smith theorem is based upon, and applications of Lurie's higher algebra, all by distinguished contributors.
Simplicial And Dendroidal Homotopy Theory
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Author : Gijs Heuts
language : en
Publisher: Springer Nature
Release Date : 2022-08-02
Simplicial And Dendroidal Homotopy Theory written by Gijs Heuts and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-02 with Mathematics categories.
This open access book offers a self-contained introduction to the homotopy theory of simplicial and dendroidal sets and spaces. These are essential for the study of categories, operads, and algebraic structure up to coherent homotopy. The dendroidal theory combines the combinatorics of trees with the theory of Quillen model categories. Dendroidal sets are a natural generalization of simplicial sets from the point of view of operads. In this book, the simplicial approach to higher category theory is generalized to a dendroidal approach to higher operad theory. This dendroidal theory of higher operads is carefully developed in this book. The book also provides an original account of the more established simplicial approach to infinity-categories, which is developed in parallel to the dendroidal theory to emphasize the similarities and differences. Simplicial and Dendroidal Homotopy Theory is a complete introduction, carefully written with the beginning researcher in mind and ideally suited for seminars and courses. It can also be used as a standalone introduction to simplicial homotopy theory and to the theory of infinity-categories, or a standalone introduction to the theory of Quillen model categories and Bousfield localization.
Derived Algebraic Geometry
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Author : Renaud Gauthier
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-01-29
Derived Algebraic Geometry written by Renaud Gauthier and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-29 with Mathematics categories.
The second edition presents schemes, simplicial sets, higher categories, model categories, derived algebraic geometry, and spectral algebraic geometry in a self-contained manner. It discusses Motives, Goodwillie Calculus, Higher Galois, Supersymmetry, and topics in physical mathematics. A new chapter on Derived Motivic Spectrais now included as is an extended introduction to Infinity Category as well as a revised chapter on Stacks.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 1987
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
Dissertation Abstracts International
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Author :
language : en
Publisher:
Release Date : 2008
Dissertation Abstracts International written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Dissertations, Academic categories.
Comprehensive Dissertation Index
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Author :
language : en
Publisher:
Release Date : 1984
Comprehensive Dissertation Index written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Dissertations, Academic categories.
Vols. for 1973- include the following subject areas: Biological sciences, Agriculture, Chemistry, Environmental sciences, Health sciences, Engineering, Mathematics and statistics, Earth sciences, Physics, Education, Psychology, Sociology, Anthropology, History, Law & political science, Business & economics, Geography & regional planning, Language & literature, Fine arts, Library & information science, Mass communications, Music, Philosophy and Religion.
Comprehensive Dissertation Index Mathematics Statistics Physics A E
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Author :
language : en
Publisher:
Release Date : 1984
Comprehensive Dissertation Index Mathematics Statistics Physics A E written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Dissertations, Academic categories.