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portada Elements of ∞-Category Theory: 194 (Cambridge Studies in Advanced Mathematics, Series Number 194)
Type
Physical Book
Author
Publisher
Year
2022
Language
English
Pages
750
Format
Hardcover
Dimensions
23.2 x 16.0 x 4.3 cm
Weight
1.18 kg.
ISBN13
9781108837989
Edition No.
1
Categories

Elements of ∞-Category Theory: 194 (Cambridge Studies in Advanced Mathematics, Series Number 194)

Emily Riehl (Author) · Dominic Verity (Author) · Cambridge University Press · Hardcover

Elements of ∞-Category Theory: 194 (Cambridge Studies in Advanced Mathematics, Series Number 194) - Riehl, Emily ; Verity, Dominic

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Synopsis "Elements of ∞-Category Theory: 194 (Cambridge Studies in Advanced Mathematics, Series Number 194) "

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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