Weak equivalence

Summary

In abstract homotopy theory, the weak equivalences of a category are the morphisms that one wants to treat as if they were isomorphisms. They form one of the three classes of a model category, and the homotopy category is obtained by inverting them. The motivating examples are the weak homotopy equivalences of topological spaces and the quasi-isomorphisms of chain complexes. A weak equivalence need not have an inverse morphism, which is why the word weak is used.