FRENCH

La Théorie de l'Homotopie de Grothendieck

Book information

Publisher
Societe Mathematique de France
Year
2012
Language
french
Format
PDF
Filesize
1 MB (1116075 bytes)
Series
Astérisque
Pages
189\189
Time added
2012-02-20 09:40:03

Description

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.

Similar books