Localization of A Category - Serre's C-theory

Serre's C-theory

Serre introduced the idea of working in homotopy theory modulo some class C of abelian groups. This meant that groups A and B were treated as isomorphic, if for example A/B lay in C. Later Dennis Sullivan had the bold idea instead of using the localization of a topological space, which took effect on the underlying topological spaces.