Elements 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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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Cambridge ; New York ; Melbourne ; New Delhi ; Singapore
Cambridge University Press
2022
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| Ausgabe: | Frist published |
| Schriftenreihe: | Cambridge studies in advanced mathematics
194 |
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Tag hinzufügen | Zusammenfassung: | 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 |
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| Beschreibung: | xix, 759 Seiten Diagramme |
| ISBN: | 9781108837989 978-1-108-83798-9 9781108936880 978-1-108-93688-0 |