Homotopy theory of enriched Mackey functors: closed multicategories, permutative enrichments, and algebraic foundations for spectral Mackey functors
This work develops techniques and basic results concerning the homotopy theory of enriched diagrams and enriched Mackey functors. Presentation of a category of interest as a diagram category has become a standard and powerful technique in a range of applications. Diagrams that carry enriched structu...
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge, United Kingdom ; New York, NY
Cambridge University Press
2025
|
| Schriftenreihe: | London Mathematical Society lecture note series
492 |
| Links: | https://doi.org/10.1017/9781009519564 |
| Zusammenfassung: | This work develops techniques and basic results concerning the homotopy theory of enriched diagrams and enriched Mackey functors. Presentation of a category of interest as a diagram category has become a standard and powerful technique in a range of applications. Diagrams that carry enriched structures provide deeper and more robust applications. With an eye to such applications, this work provides further development of both the categorical algebra of enriched diagrams, and the homotopy theoretic applications in K-theory spectra. The title refers to certain enriched presheaves, known as Mackey functors, whose homotopy theory classifies that of equivariant spectra. More generally, certain stable model categories are classified as modules - in the form of enriched presheaves - over categories of generating objects. This text contains complete definitions, detailed proofs, and all the background material needed to understand the topic. It will be indispensable for graduate students and researchers alike. |
| Umfang: | 1 Online-Ressource (xxxix, 483 Seiten) |
| ISBN: | 9781009519564 |
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| 245 | 1 | 0 | |a Homotopy theory of enriched Mackey functors |b closed multicategories, permutative enrichments, and algebraic foundations for spectral Mackey functors |c Niles Johnson, the Ohio State University at Newark, Donald Yau, the Ohio State University at Newark |
| 264 | 1 | |a Cambridge, United Kingdom ; New York, NY |b Cambridge University Press |c 2025 | |
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| 490 | 1 | |a London Mathematical Society lecture note series |v 492 | |
| 520 | |a This work develops techniques and basic results concerning the homotopy theory of enriched diagrams and enriched Mackey functors. Presentation of a category of interest as a diagram category has become a standard and powerful technique in a range of applications. Diagrams that carry enriched structures provide deeper and more robust applications. With an eye to such applications, this work provides further development of both the categorical algebra of enriched diagrams, and the homotopy theoretic applications in K-theory spectra. The title refers to certain enriched presheaves, known as Mackey functors, whose homotopy theory classifies that of equivariant spectra. More generally, certain stable model categories are classified as modules - in the form of enriched presheaves - over categories of generating objects. This text contains complete definitions, detailed proofs, and all the background material needed to understand the topic. It will be indispensable for graduate students and researchers alike. | ||
| 700 | 1 | |a Yau, Donald Y. |d 1977- | |
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| spelling | Johnson, Niles Homotopy theory of enriched Mackey functors closed multicategories, permutative enrichments, and algebraic foundations for spectral Mackey functors Niles Johnson, the Ohio State University at Newark, Donald Yau, the Ohio State University at Newark Cambridge, United Kingdom ; New York, NY Cambridge University Press 2025 1 Online-Ressource (xxxix, 483 Seiten) txt c cr London Mathematical Society lecture note series 492 This work develops techniques and basic results concerning the homotopy theory of enriched diagrams and enriched Mackey functors. Presentation of a category of interest as a diagram category has become a standard and powerful technique in a range of applications. Diagrams that carry enriched structures provide deeper and more robust applications. With an eye to such applications, this work provides further development of both the categorical algebra of enriched diagrams, and the homotopy theoretic applications in K-theory spectra. The title refers to certain enriched presheaves, known as Mackey functors, whose homotopy theory classifies that of equivariant spectra. More generally, certain stable model categories are classified as modules - in the form of enriched presheaves - over categories of generating objects. This text contains complete definitions, detailed proofs, and all the background material needed to understand the topic. It will be indispensable for graduate students and researchers alike. Yau, Donald Y. 1977- Erscheint auch als Druck-Ausgabe 9781009519526 |
| spellingShingle | Johnson, Niles Homotopy theory of enriched Mackey functors closed multicategories, permutative enrichments, and algebraic foundations for spectral Mackey functors |
| title | Homotopy theory of enriched Mackey functors closed multicategories, permutative enrichments, and algebraic foundations for spectral Mackey functors |
| title_auth | Homotopy theory of enriched Mackey functors closed multicategories, permutative enrichments, and algebraic foundations for spectral Mackey functors |
| title_exact_search | Homotopy theory of enriched Mackey functors closed multicategories, permutative enrichments, and algebraic foundations for spectral Mackey functors |
| title_full | Homotopy theory of enriched Mackey functors closed multicategories, permutative enrichments, and algebraic foundations for spectral Mackey functors Niles Johnson, the Ohio State University at Newark, Donald Yau, the Ohio State University at Newark |
| title_fullStr | Homotopy theory of enriched Mackey functors closed multicategories, permutative enrichments, and algebraic foundations for spectral Mackey functors Niles Johnson, the Ohio State University at Newark, Donald Yau, the Ohio State University at Newark |
| title_full_unstemmed | Homotopy theory of enriched Mackey functors closed multicategories, permutative enrichments, and algebraic foundations for spectral Mackey functors Niles Johnson, the Ohio State University at Newark, Donald Yau, the Ohio State University at Newark |
| title_short | Homotopy theory of enriched Mackey functors |
| title_sort | homotopy theory of enriched mackey functors closed multicategories permutative enrichments and algebraic foundations for spectral mackey functors |
| title_sub | closed multicategories, permutative enrichments, and algebraic foundations for spectral Mackey functors |
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