Michael Barr is the Peter Redpath Emeritus Professor of Pure Mathematics at McGill University. Although his earlier work was in homological algebra, his principal research area for a number of years has been category theory.
He 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. Michael Barr has much advocated the methods of his late student Jon Beck, involving monads, especially monadicity criteria and monadic cohomology.
Barr is well known to theoretical computer scientists for his book
as well as for the development of star-autonomous categories and Chu spaces which have found various applications in computer science. Also
$*$-autonomous categories,
Acyclic Models, CRM monographs, 2002,
On toposes, monads (“triples”) and algebraic theories:
On an improved context for Pontrjagin duality:
Michael Barr, On duality of topological abelian groups (pdf, pdf)
Did you know that there is a *-autonomous category of topological abelian groups that includes all the LCA groups and whose duality extends that of Pontrjagin? The groups are characterized by the property that among all topological groups on the same underlying abelian group and with the same set of continuous homomorphisms to the circle, these have the finest topology. It is not obvious that such a finest exists, but it does and that is the key.
The above material is based on
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