Samuel Eilenberg
Samuel Eilenberg was a Polish-American mathematician who co-founded category theory and homological algebra.
Early life and education
He was born in Warsaw, Kingdom of Poland to a Jewish family. He spent much of his career as a professor at Columbia University.He earned his Ph.D. from University of Warsaw in 1936, with thesis On the Topological Applications of Maps onto a Circle; his thesis advisors were Kazimierz Kuratowski and Karol Borsuk. He died in New York City in January 1998.
Career
Eilenberg's main body of work was in algebraic topology. He worked on the axiomatic treatment of homology theory with Norman Steenrod, and on homological algebra with Saunders Mac Lane. As a result of this work, Eilenberg and Mac Lane developed the field of category theory, for which they are now best known.Eilenberg was a member of Bourbaki and, with Henri Cartan, wrote the 1956 book Homological Algebra.
Later in life he worked mainly in pure category theory, being one of the founders of the field. The Eilenberg swindle is a construction applying the telescoping cancellation idea to projective modules.
Eilenberg contributed to automata theory and algebraic automata theory. In particular, he introduced a model of computation called X-machine and a new prime decomposition algorithm for finite state machines in the vein of Krohn–Rhodes theory. He also identified a natural correspondence between certain classes of regular languages called varieties and pseudovarieties of finite monoids, a result which is now known as Eilenberg's theorem.