Fibrations and Idempotent Functors
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
This thesis consists of two articles. Both articles concern homotopical algebra. In Paper I we study functors indexed by a small category into a model category whose value at each morphism is a weak equivalence. We show that the category of such functors can be understood as a certain mapping space. Specializing to topological spaces, this result is used to reprove a classical theorem that classifies fibrations with a fixed base and homotopy fiber. In Paper II we study augmented idempotent functors, i.e., co-localizations, operating on the category of groups. We relate these functors to cellular coverings of groups and show that a number of properties, such as finiteness, nilpotency etc., are preserved by such functors. Furthermore, we classify the values that such functors can take upon finite simple groups and give an explicit construction of such values.
Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. , vii, 26 p.
Trita-MAT. MA, ISSN 1401-2278 ; 11:11
IdentifiersURN: urn:nbn:se:kth:diva-66740ISBN: 978-91-7502-235-3OAI: oai:DiVA.org:kth-66740DiVA: diva2:484557
2012-01-31, Sal F3, Lindstedtsvägen 26, KTH, Stockholm, 13:00 (English)
Broto, Carles, Professor
Chachólski, Wojciech, Professor
QC 201201272012-01-272012-01-272012-02-10Bibliographically approved
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