Categorical Homotopy Theory.
This categorical perspective on homotopy theory helps consolidate and simplify one's understanding of derived functors, homotopy limits and colimits, and model categories, among others.
Saved in:
| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York :
Cambridge University Press,
2014.
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| Series: | New mathematical monographs.
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| Subjects: | |
| Online Access: | CONNECT |
MARC
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| 100 | 1 | |a Riehl, Emily. | |
| 245 | 1 | 0 | |a Categorical Homotopy Theory. |
| 260 | |a New York : |b Cambridge University Press, |c 2014. | ||
| 300 | |a 1 online resource (372 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 490 | 1 | |a New Mathematical Monographs ; |v v. 24 | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover; Half title; Series; Title; Copyright; Dedication; Epigraph; Contents; Preface; Prerequisites; Notational Conventions; Acknowledgments; Part I Derived functors and homotopy (co)limits; 1 All concepts are Kan extensions; 1.1 Kan extensions; 1.2 A formula; 1.3 Pointwise Kan extensions; 1.4 All concepts; 1.5 Adjunctions involving simplicial sets; 2 Derived functors via deformations; 2.1 Homotopical categories and derived functors; 2.2 Derived functors via deformations; 2.3 Classical derived functors between abelian categories; 2.4 Preview of homotopy limits and colimits. | |
| 505 | 8 | |a 3 Basic concepts of enriched category theory3.1 A first example; 3.2 The base for enrichment; 3.3 Enriched categories; 3.4 Underlying categories of enriched categories; 3.5 Enriched functors and enriched natural transformations; 3.6 Simplicial categories; 3.7 Tensors and cotensors; 3.8 Simplicial homotopy and simplicial model categories; 4 The unreasonably effective (co)bar construction; 4.1 Functor tensor products; 4.2 The bar construction; 4.3 The cobar construction; 4.4 Simplicial replacements and colimits; 4.5 Augmented simplicial objects and extra degeneracies. | |
| 505 | 8 | |a 5 Homotopy limits and colimits: The theory5.1 The homotopy limit and colimit functors; 5.2 Homotopical aspects of the bar construction; 6 Homotopy limits and colimits: The practice; 6.1 Convenient categories of spaces; 6.2 Simplicial model categories of spaces; 6.3 Warnings and simplifications; 6.4 Sample homotopy colimits; 6.5 Sample homotopy limits; 6.6 Homotopy colimits as weighted colimits; Part II Enriched homotopy theory; 7 Weighted limits and colimits; 7.1 Weighted limits in unenriched category theory; 7.2 Weighted colimits in unenriched category theory. | |
| 505 | 8 | |a 7.3 Enriched natural transformations and enriched ends7.4 Weighted limits and colimits; 7.5 Conical limits and colimits; 7.6 Enriched completeness and cocompleteness; 7.7 Homotopy (co)limits as weighted (co)limits; 7.8 Balancing bar and cobar constructions; 8 Categorical tools for homotopy (co)limit computations; 8.1 Preservation of weighted limits and colimits; 8.2 Change of base for homotopy limits and colimits; 8.3 Final functors in unenriched category theory; 8.4 Final functors in enriched category theory; 8.5 Homotopy final functors; 9 Weighted homotopy limits and colimits. | |
| 505 | 8 | |a 9.1 The enriched bar and cobar construction9.2 Weighted homotopy limits and colimits; 10 Derived enrichment; 10.1 Enrichments encoded as module structures; 10.2 Derived structures for enrichment; 10.3 Weighted homotopy limits and colimits, revisited; 10.4 Homotopical structure via enrichment; 10.5 Homotopy equivalences versus weak equivalences; Part III Model categories and weak factorization systems; 11 Weak factorization systems in model categories; 11.1 Lifting problems and lifting properties; 11.2 Weak factorization systems; 11.3 Model categories and Quillen functors. | |
| 520 | |a This categorical perspective on homotopy theory helps consolidate and simplify one's understanding of derived functors, homotopy limits and colimits, and model categories, among others. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 546 | |a English. | ||
| 500 | |a EBSCO eBook Academic Comprehensive Collection North America |5 TMurS | ||
| 650 | 0 | |a Homotopy theory. | |
| 650 | 0 | |a Algebra, Homological. | |
| 730 | 0 | |a WORLDSHARE SUB RECORDS | |
| 758 | |i has work: |a Categorical homotopy theory (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFVfXC3HTqDccWGTtCVRyq |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Riehl, Emily. |t Categorical Homotopy Theory. |d New York : Cambridge University Press, ©2014 |z 9781107048454 |
| 830 | 0 | |a New mathematical monographs. | |
| 856 | 4 | 0 | |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=761515&authtype=ip,sso&custid=s4672406 |z CONNECT |3 eBooks on EBSCOhost |t 0 |
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