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, as in nonabelian algebraic topology, and in particular the theory of closed model categories.This subject has received much attention in recent years due to new foundational work of Vladimir Voevodsky, Eric Friedlander, Andrei Suslin, and others resulting in the 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 Markus Rost, the full Bloch–Kato conjecture. At first, homotopy theory was restricted to topological spaces, while homological algebra worked in a variety of (mainly algebraic) examples. Whitehead proposed around 1949 the subject of algebraic homotopy theory, to deal with classical homotopy theory of spaces via algebraic models. This idea did not extend to homotopy methods in general setups of course, but it had concrete modelling and calculations for topological spaces in mind. In the 1960s Grothendieck introduced fundamental groups and cohomology in the setup of topoi, which were a wider and more modern setup. In retrospective, he considered exactness axioms which he introduced in Tohoku in a context of homological algebra to be conceptually a kind of reasoning bringing understanding to general spaces, such as topoi