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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.

Categories (Mathematics). --- Model theory. --- Representations of categories. --- Toposes. --- Categories (Mathematics) --- Algebra --- Mathematics --- Physical Sciences & Mathematics --- Algebra, Homological. --- Homological algebra --- Category theory (Mathematics) --- Mathematics. --- Category theory (Mathematics). --- Homological algebra. --- Topology. --- Algebraic topology. --- Category Theory, Homological Algebra. --- Algebraic Topology. --- Algebra, Abstract --- Homology theory --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Algebra. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Mathematical analysis

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Representations of groups. --- Categories (Mathematics) --- Représentations de groupes --- Catégories (Mathématiques) --- Group theory --- Representations of groups --- 51 <082.1> --- Group representation (Mathematics) --- Groups, Representation theory of --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Mathematics--Series

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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.

Category theory. Homological algebra --- Algebraic topology --- Topology --- algebra --- topologie (wiskunde) --- wiskunde --- topologie

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The year's finest mathematical writing from around the worldThis annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2020 makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday aspects of math, and take readers behind the scenes of today’s hottest mathematical debates.Here, Steven Strogatz reveals how calculus drives advances in virology, Paul Thagard argues that the power of mathematics stems from its combination of realistic and fictional qualities, and Erica Klarreich describes how Hao Huang used the combinatorics of cube nodes to solve a longstanding problem in computer science. In other essays, John Baez tells how he discovered the irresistible attractions of algebraic geometry, Mark Colyvan compares the radically different explanatory practices of mathematics and science, and Boris Odehnal reviews some surprising properties of multidimensional geometries. And there’s much, much more.In addition to presenting the year’s most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor.This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.

Mathematics --- articles. --- collection. --- epidemiology. --- essays. --- journals. --- magazines. --- math. --- mathematics. --- papers. --- pieces. --- selection. --- stories. --- virus.