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**Michael Barr** (born January 22, 1937) is an American mathematician who is the Peter Redpath Emeritus Professor of Pure Mathematics at McGill University.^{[1]}

Michael Barr | |
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Born | Philadelphia, Pennsylvania, U.S. | January 22, 1937

Academic background | |

Education | University of Pennsylvania (BS, PhD) |

Academic work | |

Discipline | Mathematics |

Sub-discipline | Homological algebra Category theory Theoretical computer science |

Institutions | Columbia University University of Illinois Urbana-Champaign McGill University |

He was born in Philadelphia, Pennsylvania, and graduated from the 202nd class of Central High School in June 1954. He graduated from the University of Pennsylvania in February 1959 and received a PhD from the same school in June 1962.

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*). He was then an instructor at Columbia University and from 1964 Assistant Professor and later Associate Professor at the University of Illinois Urbana-Champaign. In 1968 he became Associate Professor and in 1972 Professor at McGill University.

In 1967 and 1975/76 he was a visiting scientist at ETH Zurich and in 1970/71 at the University of Fribourg and in 1989/90 a visiting professor at the University of Pennsylvania.

In 1970 he was an invited speaker at the International Congress of Mathematicians in Nice *(Non-abelian full embedding: outline*).

His earlier work was in homological algebra, but his principal research area for a number of years has been category theory. He is well known to theoretical computer scientists for his book *Category Theory for Computing Science* (1990) with Charles Wells, as well as for the development of *-autonomous categories and Chu spaces which have found various applications in computer science. 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.

Barr is on the editorial boards of *Mathematical Structures in Computer Science* and the electronic journal *Homology, Homotopy and Applications*, and is editor of the electronic journal *Theory and Applications of Categories*.

**^**"Mathematics and Statistics". McGill University. Retrieved 11 August 2011.**^**Pitts, Andrew (March 1991), "Review of Toposes, Triples and Theories by Barr, M., & Wells, C.",*Journal of Symbolic Logic*,**56**(1): 340–341, doi:10.2307/2274934**^**Rota, Gian-Carlo (August 1986), "Toposes, triples and theories: M. Barr and C. Wells, Springer, 1985, 345 pp.",*Advances in Mathematics*,**61**(2): 184, doi:10.1016/0001-8708(86)90076-9

*Toposes, Triples and Theories*, updated edition of text first published in 1985.*Category Theory for Computing Science*, updated 3rd edition of the book.- Some aspects of homological Algebra, translation of Grothendieck's
*Tôhoku*paper - http://www.tac.mta.ca/tac (Theory and Applications of Categories)
- https://web.archive.org/web/20080704125156/http://www.math.rutgers.edu/hha/geninfo.html (Homology, Homotopy and Applications)
- Michael Barr at the Mathematics Genealogy Project