Adams Representability in Triangulated Categories
[eng] This thesis contains new results about the representability of cohomological functors defined on a subcategory of compact objects (with respect to a fixed cardinal) of a well generated triangulated category. Classical theorems of Adams for the stable homotopy category and Neeman for compactly...
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| Format: | doctoral thesis |
| Status: | Published version |
| Publication Date: | 2011 |
| Country: | España |
| Institution: | Universidad de Barcelona |
| Repository: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/35159 |
| Online Access: | https://hdl.handle.net/2445/35159 http://www.tdx.cat/TDX-0324111-094914 http://hdl.handle.net/10803/682 |
| Access Level: | Open access |
| Keyword: | Categories abelianes Teoria de l'homotopia Àlgebra homològica Abelian categories Homotopy theory Algebra, Homological |
| Summary: | [eng] This thesis contains new results about the representability of cohomological functors defined on a subcategory of compact objects (with respect to a fixed cardinal) of a well generated triangulated category. Classical theorems of Adams for the stable homotopy category and Neeman for compactly generated triangulated categories are extended to the first uncountable cardinal. The case of derived categories of rings and the stable motivic category are studied in detail. These results contribute to answering negatively a question raised by Rosický of whether all cohomological functors defined on a subcategory of compact objects with respect to a large enough cardinal are representable. Some of the findings in this thesis are based on new results about abelian categories, the most relevant being a generalization of the Auslander Lemma for non Grothendieck categories. |
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