Elements of [infinity]-category theory
著者
書誌事項
Elements of [infinity]-category theory
（Cambridge studies in advanced mathematics, 194）
Cambridge University Press, 2022
- : hardback
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注記
Includes bibliographical references (p. 733-739) and index
内容説明・目次
内容説明
The language of -categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an -category is requires various technical models, raising the question of how they might be compared. To overcome this, a model-independent approach is desired, so that theorems proven with any model would apply to them all. This text develops the theory of -categories from first principles in a model-independent fashion using the axiomatic framework of an -cosmos, the universe in which -categories live as objects. An -cosmos is a fertile setting for the formal category theory of -categories, and in this way the foundational proofs in -category theory closely resemble the classical foundations of ordinary category theory. Equipped with exercises and appendices with background material, this first introduction is meant for students and researchers who have a strong foundation in classical 1-category theory.
目次
- 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.
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