Overview
- Postulates a model of weak n-categories using structures (called n-fold categories) with strictly associative compositions
- Encompasses intuitive introductions to new concepts, which would otherwise remain very technical
- Provides diagrammatic summaries and road-maps to guide the reader
- Offers a very thorough introduction to multi-simplicial techniques, including figures illustrating geometric interpretations in low dimensions
Part of the book series: Algebra and Applications (AA, volume 26)
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Table of contents (13 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
“This book is a research monograph and is primarily aimed primarily at professionals and advanced graduate students working in topology or category theory. It would also be useful to those working in theoretical physics or algebraic geometry who use higher category methods. … The author’s solution to the homotopy hypothesis is appealing as well as geometrically and categorically insightful.” (MAA Reviews, April 7, 2020)
Authors and Affiliations
About the author
Simona Paoli has been active in the field of higher category theory for fifteen years and she has a very strong track record of innovation in this area. She is an expert in the use of multi-simplicial techniques in higher category theory and in applications to homotopy theory. She collaborated extensively with leading researchers both in category theory and in algebraic topology.
Bibliographic Information
Book Title: Simplicial Methods for Higher Categories
Book Subtitle: Segal-type Models of Weak n-Categories
Authors: Simona Paoli
Series Title: Algebra and Applications
DOI: https://doi.org/10.1007/978-3-030-05674-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-05673-5Published: 14 June 2019
eBook ISBN: 978-3-030-05674-2Published: 03 June 2019
Series ISSN: 1572-5553
Series E-ISSN: 2192-2950
Edition Number: 1
Number of Pages: XXII, 343
Number of Illustrations: 250 b/w illustrations, 12 illustrations in colour
Topics: Category Theory, Homological Algebra, Algebraic Topology, Mathematical Physics, Algebraic Geometry