Elements of [infinity]-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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| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge ; New York, NY
Cambridge University Press
2022
|
| Series: | Cambridge Studies in Advanced Mathematics
194 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | 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 |
| Item Description: | 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 |
| Physical Description: | 1 Online-Ressource (xix, 759 Seiten) |
| ISBN: | 9781108936880 |
| DOI: | 10.1017/9781108936880 |
Staff View
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| author | Riehl, Emily 1983- Verity, Dominic 1966- |
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| institution | BVB |
| isbn | 9781108936880 |
| language | English |
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| spelling | Riehl, Emily 1983- (DE-588)1058749897 aut Elements of [infinity]-category theory Emily Riehl, Dominic Verity Cambridge ; New York, NY Cambridge University Press 2022 1 Online-Ressource (xix, 759 Seiten) txt rdacontent c rdamedia cr rdacarrier 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 Categories (Mathematics) Infinite groups Unendliche Gruppe (DE-588)4375539-2 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 s Unendliche Gruppe (DE-588)4375539-2 s DE-604 Kategorie Mathematik (DE-588)4129930-9 s Verity, Dominic 1966- (DE-588)1147049335 aut Erscheint auch als Druck-Ausgabe 978-1-108-83798-9 https://doi.org/10.1017/9781108936880 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Riehl, Emily 1983- Verity, Dominic 1966- Elements of [infinity]-category theory Categories (Mathematics) Infinite groups Unendliche Gruppe (DE-588)4375539-2 gnd Kategorientheorie (DE-588)4120552-2 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| subject_GND | (DE-588)4375539-2 (DE-588)4120552-2 (DE-588)4129930-9 |
| title | Elements of [infinity]-category theory |
| title_auth | Elements of [infinity]-category theory |
| title_exact_search | Elements of [infinity]-category theory |
| title_exact_search_txtP | Elements of [infinity]-category theory |
| title_full | Elements of [infinity]-category theory Emily Riehl, Dominic Verity |
| title_fullStr | Elements of [infinity]-category theory Emily Riehl, Dominic Verity |
| title_full_unstemmed | Elements of [infinity]-category theory Emily Riehl, Dominic Verity |
| title_short | Elements of [infinity]-category theory |
| title_sort | elements of infinity category theory |
| topic | Categories (Mathematics) Infinite groups Unendliche Gruppe (DE-588)4375539-2 gnd Kategorientheorie (DE-588)4120552-2 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| topic_facet | Categories (Mathematics) Infinite groups Unendliche Gruppe Kategorientheorie Kategorie Mathematik |
| url | https://doi.org/10.1017/9781108936880 |
| work_keys_str_mv | AT riehlemily elementsofinfinitycategorytheory AT veritydominic elementsofinfinitycategorytheory |