He is known for work in algebraic topology, in particular on cohomology operations, killing homotopy groups and group cohomology. His seminar in Paris in the years after 1945 covered ground on several complex variables, sheaf theory, spectral sequences and homological algebra, in a way that deeply influenced Jean-Pierre Serre, Armand Borel, Alexander Grothendieck and Frank Adams, amongst others of the leading lights of the younger generation.

He also took part in the Bourbaki group. His book with Samuel Eilenberg *Homological Algebra* (1956) was an important text, treating the subject with a moderate level of abstraction and category theory.