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The language of -categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. This book develops a new, more accessible model-independent approach to the foundations of -category theory by studying the universe, or -cosmos, in which -categories live.
List of contents
Part I. Basic ¿-Category Theory: 1. ¿-Cosmoi and their homotopy 2-categories; 2. Adjunctions, limits, and colimits I; 3. Comma ¿-categories; 4. Adjunctions, limits, and colimits II; 5. Fibrations and Yoneda's lemma; 6. Exotic ¿-cosmoi; Part II. The Calculus of Modules: 7. Two-sided fibrations and modules; 8. The calculus of modules; 9. Formal category theory in a virtual equipment; Part III. Model Independence: 10. Change-of-model functors; 11. Model independence; 12. Applications of model independence.
About the author
Emily Riehl is an associate professor of mathematics at Johns Hopkins University. She received her PhD from the University of Chicago and was a Benjamin Peirce and NSF postdoctoral fellow at Harvard University. She is the author of Categorical Homotopy Theory (Cambridge, 2014) and Category Theory in Context (2016), and a co-author of Fat Chance: Probability from 0 to 1 (Cambridge, 2019). She and her present co-author have published ten articles over the course of the past decade that develop the new mathematics appearing in this book.Dominic Verity is a professor of mathematics at Macquarie University in Sydney and is a director of the Centre of Australian Category Theory. While he is a leading proponent of 'Australian-style' higher category theory, he received his PhD from the University of Cambridge and migrated to Australia in the early 1990s. Over the years he has pursued a career that has spanned the academic and non-academic worlds, working at times as a computer programmer, quantitative analyst, and investment banker. He has also served as the Chair of the Academic Senate of Macquarie University, the principal academic governance and policy body.
Summary
The language of 8-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. This book develops a new, more accessible model-independent approach to the foundations of 8-category theory by studying the universe, or 8-cosmos, in which 8-categories live.
