Elements of ∞-category theory [E-Book] / Emily Riehl, Dominic Verity
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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Full text |
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Personal Name(s): | Riehl, Emily, author |
Verity, Dominic, author | |
Imprint: |
Cambridge :
Cambridge University Press,
2022
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Physical Description: |
1 online resource (770 pages) |
Note: |
englisch |
ISBN: |
9781108936880 |
Series Title: |
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Cambridge Studies in Advanced Mathematics ;
194 |
Keywords: |
Mathematics (general), Mathematics, Logic, Categories and Sets, Geometry and Topology |
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. |