Elements of ∞-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...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York ; Melbourne ; New Delhi ; Singapore
Cambridge University Press
2022
|
| Ausgabe: | Frist published |
| Schriftenreihe: | Cambridge studies in advanced mathematics
194 |
| Schlagworte: | |
| Zusammenfassung: | 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 |
| Beschreibung: | xix, 759 Seiten Diagramme |
| ISBN: | 9781108837989 9781108936880 |
Internformat
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| 490 | 1 | |a Cambridge studies in advanced mathematics |v 194 | |
| 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 | ||
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Datensatz im Suchindex
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| author | Riehl, Emily 1983- Verity, Dominic 1966- |
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| building | Verbundindex |
| bvnumber | BV048238684 |
| classification_rvk | SK 320 |
| classification_tum | MAT 180 |
| ctrlnum | (OCoLC)1334058230 (DE-599)BVBBV048238684 |
| dewey-full | 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 |
| dewey-search | 512/.55 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | Frist published |
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| id | DE-604.BV048238684 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T19:53:21Z |
| indexdate | 2024-07-10T09:32:48Z |
| institution | BVB |
| isbn | 9781108837989 9781108936880 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033619237 |
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| physical | xix, 759 Seiten Diagramme |
| publishDate | 2022 |
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| publisher | Cambridge University Press |
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| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Riehl, Emily 1983- (DE-588)1058749897 aut Elements of ∞-category theory Emily Riehl ; The Johns Hopkins University ; Dominic Verity ; Macquarie University, Sydney Elements of [infinity]-category theory Frist published Cambridge ; New York ; Melbourne ; New Delhi ; Singapore Cambridge University Press 2022 xix, 759 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 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 Categories (Mathematics) Infinite groups Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Unendliche Gruppe (DE-588)4375539-2 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 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 Online-Ausgabe, epub 978-1-108-93688-0 Cambridge studies in advanced mathematics 194 (DE-604)BV000003678 194 |
| spellingShingle | Riehl, Emily 1983- Verity, Dominic 1966- Elements of ∞-category theory Cambridge studies in advanced mathematics Categories (Mathematics) Infinite groups Kategorie Mathematik (DE-588)4129930-9 gnd Unendliche Gruppe (DE-588)4375539-2 gnd Kategorientheorie (DE-588)4120552-2 gnd |
| subject_GND | (DE-588)4129930-9 (DE-588)4375539-2 (DE-588)4120552-2 |
| title | Elements of ∞-category theory |
| title_alt | Elements of [infinity]-category theory |
| title_auth | Elements of ∞-category theory |
| title_exact_search | Elements of ∞-category theory |
| title_exact_search_txtP | Elements of ∞-category theory |
| title_full | Elements of ∞-category theory Emily Riehl ; The Johns Hopkins University ; Dominic Verity ; Macquarie University, Sydney |
| title_fullStr | Elements of ∞-category theory Emily Riehl ; The Johns Hopkins University ; Dominic Verity ; Macquarie University, Sydney |
| title_full_unstemmed | Elements of ∞-category theory Emily Riehl ; The Johns Hopkins University ; Dominic Verity ; Macquarie University, Sydney |
| title_short | Elements of ∞-category theory |
| title_sort | elements of ∞ category theory |
| topic | Categories (Mathematics) Infinite groups Kategorie Mathematik (DE-588)4129930-9 gnd Unendliche Gruppe (DE-588)4375539-2 gnd Kategorientheorie (DE-588)4120552-2 gnd |
| topic_facet | Categories (Mathematics) Infinite groups Kategorie Mathematik Unendliche Gruppe Kategorientheorie |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT riehlemily elementsofcategorytheory AT veritydominic elementsofcategorytheory AT riehlemily elementsofinfinitycategorytheory AT veritydominic elementsofinfinitycategorytheory |