Homotopical algebra
From Wikipedia, the free encyclopedia
In mathematics, homotopical algebra is a collection of concepts comprising the nonabelian aspects of homological algebra as well as possibly the abelian aspects as special cases. The homotopical nomenclature stems from the fact that a common approach to such generalizations is via abstract homotopy theory and in particular the theory of closed model categories.
This subject has received much attention in recent years due to new foundational work of Voevodsky, Friedlander, Suslin, and others resulting in the A1 homotopy theory for quasiprojective varieties over a field. Voevodsky has used this new algebraic homotopy theory to prove the Milnor conjecture (for which he was awarded the Fields Medal) and later, in collaboration with M. Rost, the full Bloch-Kato conjecture.
[edit] External links
 |
This geometry-related article is a stub. You can help Wikipedia by expanding it. |
 |
This topology-related article is a stub. You can help Wikipedia by expanding it. |
