Codescent theory I: Foundations
| Autor: | Michel Matthey, Paul Balmer |
|---|---|
| Rok vydání: | 2004 |
| Předmět: |
Pure mathematics
Property (philosophy) Model category Structure (category theory) Isomorphism-closed subcategory 01 natural sciences Set (abstract data type) Mathematics::K-Theory and Homology Mathematics::Category Theory 0103 physical sciences FOS: Mathematics Algebraic Topology (math.AT) Category Theory (math.CT) Mathematics - Algebraic Topology 0101 mathematics Mathematics Subcategory Functor 010102 general mathematics Mathematics - Category Theory K-Theory and Homology (math.KT) 16. Peace & justice Algebra Closed category Mathematics - K-Theory and Homology 010307 mathematical physics Geometry and Topology |
| Zdroj: | Topology and its Applications. 145(1-3):11-59 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2004.05.009 |
| Popis: | Consider a cofibrantly generated model category $S$, a small category $C$ and a subcategory $D$ of $C$. We endow the category $S^C$ of functors from $C$ to $S$ with a model structure, defining weak equivalences and fibrations objectwise but only on $D$. Our first concern is the effect of moving $C$, $D$ and $S$. The main notion introduced here is the ``$D$-codescent'' property for objects in $S^C$. Our long-term program aims at reformulating as codescent statements the Conjectures of Baum-Connes and Farrell-Jones, and at tackling them with new methods. Here, we set the grounds of a systematic theory of codescent, including pull-backs, push-forwards and various invariance properties. Comment: 48 pages (minor changes in the presentation and the references) |
| Databáze: | OpenAIRE |
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