Elements of ∞-Category Theory

ISBN-13: 9781108837989 / Angielski / Twarda / 2022 / 750 str.

Sydney) Verity Dominic (Macquarie University

Opis

This book develops the theory of infinite-dimensional categories by studying the universe, or ∞-cosmos, in which they live.

Recenzje

'This remarkable book starts with the premise that it should be possible to study ∞-categories armed only with the tools of 2-category theory. It is the result of the authors' decade-long collaboration, and they have poured into it all their experience, technical brilliance, and expository skill. I'm sure I'll be turning to it for many years to come.' Steve Lack, Macquarie University

Spis treści

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.