@book{a2d40278d3964661860d7b616fca0199,

title = "Elements of ∞-category theory",

abstract = "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.",

keywords = "Mathematics (general), Mathematics, Logic, Categories and Sets, Geometry and Topology",

author = "Emily Riehl and Dominic Verity",

note = "This book has been reviewed and is under contract to Cambridge University Press, with final draft due for submission by the end of March 2021.",

year = "2022",

doi = "10.1017/9781108936880",

language = "English",

isbn = "9781108837989",

series = "Cambridge studies in advanced mathematics",

publisher = "Cambridge University Press (CUP)",

address = "United Kingdom",

}