Michael Barr (born January 22, 1937) is an American mathematician who is the Peter Redpath Emeritus Professor of Pure Mathematics at McGill University.
Barr studied mathematics at the University of Pennsylvania, graduating with a bachelor's degree in 1959 and a doctorate in 1962 under David Kent Harrison (Cohomology of Commutative Algebras).
His earlier work was in homological algebra, but his principal research area for a number of years has been category theory.
His monograph *-autonomous categories (1979), and his books Toposes, Triples, and Theories (1985),[2][3] also coauthored with Wells, and Acyclic Models (2002), are aimed at more specialized audiences.
In 2011 Michael Barr and his wife Marcia published an English translation of Grothendieck's fundamental Tôhoku paper.