This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the rig...(展开全部)

The writing bears the marks of authority of a mathematician who was actively involved in setting up the subject. Most of the papers referred to are at least twenty years old but this reflects the time when the ideas were established and one imagines that the situation will be different in the second volume. Because of the length, it is unlikely that many people will read this b...(展开全部)

The writing bears the marks of authority of a mathematician who was actively involved in setting up the subject. Most of the papers referred to are at least twenty years old but this reflects the time when the ideas were established and one imagines that the situation will be different in the second volume. Because of the length, it is unlikely that many people will read this b...(展开全部)

Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topol...(展开全部)

Homotopy type theory is a new branch of mathematics that combines aspects of several different fields in a surprising way. It is based on a recently discovered connection between homotopy theory and type theory. It touches on topics as seemingly distant as the homotopy groups of spheres, the algorithms for type checking, and the definition of weak ∞-groupoids. Homotopy type the...(展开全部)

Homotopy type theory is a new branch of mathematics that combines aspects of several different fields in a surprising way. It is based on a recently discovered connection between homotopy theory and type theory. It touches on topics as seemingly distant as the homotopy groups of spheres, the algorithms for type checking, and the definition of weak ∞-groupoids. Homotopy type the...(展开全部)

Praise for the Second Edition: "A must-have book for anyone expecting to do research and/or applications in categorical data analysis". ("Statistics in Medicine"). "It is a total delight reading this book". ("Pharmaceutical Research"). "If you do any analysis of categorical data, this is an essential desktop reference". ("Technometrics"). The use of statistical methods for anal...(展开全部)

Praise for the Second Edition: "A must-have book for anyone expecting to do research and/or applications in categorical data analysis". ("Statistics in Medicine"). "It is a total delight reading this book". ("Pharmaceutical Research"). "If you do any analysis of categorical data, this is an essential desktop reference". ("Technometrics"). The use of statistical methods for anal...(展开全部)