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 algebraic 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 .

Reference

An abstract for a talk on the proof of the full Bloch-Kato conjecture