# Saunders Mac Lane

**Saunders Mac Lane** (4 August 1909 - 14 April 2005) was a US mathematician. He cofounded category theory with Samuel Eilenberg.

Mac Lane was born in Taftville, Connecticut. He studied at Yale University from 1926 to 1930 before going to the University of Chicago on a one-year fellowship. He was in Göttingen from 1931 to 1933, returning afterwards to a one-year position at Yale. He then became an instructor at Harvard University, followed by another one-year post – this time at Cornell in 1936. He briefly returned to Chicago in 1937, before taking a position at Harvard University as assistant professor in 1938. In 1941 Mac Lane and Garrett Birkhoff published their influential *A Survey of Modern Algebra*. After working in applied mathematics during the war years, he was a professor at Chicago from 1947.

After a thesis in mathematical logic, 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–Mac Lane spaces K(*G*,*n*), having a single non-trivial homotopy group *G* 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; in particular, *Categories for the Working Mathematician* remains the definitive introduction to category theory.

## External links

- O'Connor, John J., and Edmund F. Robertson. "Saunders Mac Lane".
*MacTutor History of Mathematics archive*. - Obituary press release from the University of Chicago
- Pictures of Mac Lane from 1984 to 1999

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