Screen LibraryElements of ∞-category theory /
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 over...
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| Published: |
Cambridge University Press,
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| Publisher Address: | Cambridge, United Kingdom : |
| Publication Dates: | 2022. |
| Literature type: | Book |
| Language: | English |
| Series: |
Cambridge studies in advanced mathematics ;
194 |
| Subjects: | |
| Summary: |
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. |
| Item Description: | In title "[infinity]" appears as the infinity symbol. |
| Carrier Form: | xix, 759 pages : illustrations ; 24 cm. |
| Bibliography: | Includes bibliographical references (pages 733-739) and index. |
| ISBN: |
9781108837989 1108837980 |
| Index Number: | QA169 |
| CLC: | O154.1 |
| Call Number: | O154.1/R555 |
| Contents: | [Infinity]-Cosmoi and their homotopy 2-categories -- Adjunctions, limits, and colimits I -- Comma [infinity]-categories -- Adjunctions, limits, and colimits II -- Fibrations and Yoneda's lemma -- Exotic [infinity]-cosmoi -- Two-sided fibrations and modules -- The calculus of modules -- Formal category theory in a virtual equipment -- Change-of-model functors -- Model independence -- Applications of model independence. |