[3] It removed the need to distinguish the cases of modules over a ring and sheaves of abelian groups over a topological space.
Research there allowed him to put homological algebra on an axiomatic basis, by introducing the abelian category concept.
[5][6] A textbook treatment of homological algebra, "Cartan–Eilenberg" after the authors Henri Cartan and Samuel Eilenberg, appeared in 1956.
[11] The Tôhoku paper also introduced the Grothendieck spectral sequence associated to the composition of derived functors.
[12] In further reconsideration of the foundations of homological algebra, Grothendieck introduced and developed with Jean-Louis Verdier the derived category concept.