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About La Théorie de l'Homotopie de Grothendieck
The aim of this book is toexplain the very beautiful homotopy theory developed by Grothendieck in \PursuingStacks". The question is to characterize categories of presheaves that modelize ho-motopy types, thus generalizing the theory of simplicial sets. The criteria discoveredby Grothendieck show that there are pretty many such categories, called elementarymodelizers. We describe a categorical construction of left homotopy Kan extensions,generalizing a construction of homotopy colimits by Thomason. We study two re-markable classes of functors, proper and smooth functors, these two notions beingmutually dual. These functors are characterized by cohomological properties inspiredby the proper or smooth base change theorem in algebraic geometry.
Detailed Information
| Author: | Georges Maltsiniotis |
|---|---|
| Publication Year: | 2012 |
| ISBN: | 790508 |
| Pages: | 189 |
| Language: | French |
| File Size: | 1.064 |
| Format: | |
| Price: | FREE |
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