Homotopical Algebra | Open Access Journals

Journal of Applied & Computational Mathematics

ISSN: 2168-9679

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Homotopical Algebra

Homotopic algebra in mathematics is a set of principles that include the nonabelian aspects of homological algebra as well as probably the abelian aspects as special cases. The homotopic nomenclature stems from the fact that a common approach to such generalizations is through the theory of abstract homotopy, as in nonabelian algebraic topology, and particularly the theory of closed model categories. Due to new fundamental research by Vladimir Voevodsky, Eric Friedlander, Andrei Suslin and others, this topic has received much attention in recent years , culminating in the A1 homotopy theory for quasiprojective varieties over a field. Voevodsky used this new theory of algebraic homotopy to prove Milnor 's theorem (for which he received the Fields Medal) and later, in collaboration with Marku the full Bloch–Kato conjecture.

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