Saunders Mac Lane (born 4 August 1909) is a US mathematician. He is one of the founders of category theory.
Mac Lane was born in Taftville, Connecticut. He studied at the Yale University from 1926 to 1930 before going to the University of Chicago on a one-year fellowship. He was in Göttingen 1931-1933, returning to a one-year position at Yale. He then became an instructor at Harvard University, followed by a one-year post at Cornell in 1936-1937. He was again at Chicago in 1937-1938; and took a position at Harvard University as assistant professor in 1938. In 1941 his Survey of Modern Algebra, written with Garrett Birkhoff.
After working in applied mathematics during the war years, he was professor at Chicago from 1947.
His first works were in field theory and valuation theory. He wrote on valuation rings and Witt vectors, and separability in infinite field extensions.
He started writing on group extensions in 1942, and collaborated with Samuel Eilenberg from 1943, on what are now called Eilenberg-MacLane spaces K(π,n), having a single non-trivial homotopy group (π, in dimension n). This work opened the way to group cohomology in general.
After the introduction via the Eilenberg-Steenrod axioms of the abstract approach to homology theory, he became one of the developers of category theory. He is known particularly for his work on coherence theorems, and his textbooks.