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Elements of [infinity]-category theory /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Elements of [infinity]-category theory // Emily Riehl, Dominic Verity.
Author:	Riehl, Emily,
other author:	Verity, Dominic,
Description:	1 online resource (xix, 759 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 21 Jan 2022).
Subject:	Categories (Mathematics) -
Online resource:	https://doi.org/10.1017/9781108936880
ISBN:	9781108936880 (ebook)

Elements of [infinity]-category theory /
Riehl, Emily,

Elements of [infinity]-category theory /Emily Riehl, Dominic Verity. - 1 online resource (xix, 759 pages) :digital, PDF file(s). - Cambridge Studies in Advanced Mathematics ;194. - Cambridge Studies in Advanced Mathematics ;194..

Title from publisher's bibliographic system (viewed on 21 Jan 2022).

[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.

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.

ISBN: 9781108936880 (ebook)Subjects--Topical Terms:

580337
Categories (Mathematics)

LC Class. No.: QA169 / .R55 2022

Dewey Class. No.: 512/.55

Elements of [infinity]-category theory /
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500 $a Title from publisher's bibliographic system (viewed on 21 Jan 2022).
505 0 $a [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.
520 $a 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.
650 0 $a Categories (Mathematics) $3 580337
650 0 $a Infinite groups. $3 579346
700 1 $a Verity, Dominic, $d 1966- $e author. $3 1446020
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830 0 $a Cambridge Studies in Advanced Mathematics ; $v 194. $3 1446021
856 4 0 $u https://doi.org/10.1017/9781108936880