''m'' ''n'' cyclically follow '' delta '' sub ''n'' sub certain homomorphisms determined ''f'' ''g'' called '''connecting homomorphisms''' topological manifestations theorem include mayer vietoris sequence long exact sequence relative homology foundational aspects cohomology theories defined many different objects topological spaces sheaves groups rings lie algebras c algebras study modern algebraic geometry would almost unthinkable without sheaf cohomology central homological algebra notion exact sequence used perform actual calculations classical tool homological algebra
Formal science Mathematics Pure mathematics Algebra Homological algebra