nLab Michael Barr

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.

Selected writings

See also:

  • personal list of publications: web page

On Hochschild cohomology of commutative algebras:

  • Michael Barr, Cohomology of commutative algebra I, Ph.D. Thesis, University of Pennsylvania (1962), Retyped with a few corrections and notes (2003) [pdf, pdf]

see also

and in relation to monadic cohomology:

On monads in universal algebra and (co-)homology-theory:

On cohomology of algebraic-structures (such as Lie algebra cohomology) via monads (“triples”, cf. monadic cohomology and canonical resolution):

On comonadicity of free monadic algebra-functors:

  • Michael Barr, Coalgebras in a category of algebras, in: Category Theory, Homology Theory and their Applications I, Lecture Notes in Mathematics 86, Springer (1969) 1-12 [doi:10.1007/BFb0079381, pdf, pdf]

Introducing Barr-exact categories and regular categories:

On coalgebras over a commutative ring (cf. CocommCoalg):

On right exact functors:

On topoi without topos points:

On the abstract construction principle behind cartesian closed convenient categories of topological spaces (such as compactly generated topological spaces):

Introducing star-autonomous categories:

On Galois theory:

On atomic toposes:

On toposes, monads (“triples”) and algebraic theories:

Exposition of sheaf toposes:

On models of Horn theories:

  • Michael Barr, Models of Horn theories, in: Categories in Computer Science and Logic, Contemporary Math. 92, Amer. Math. Soc. (1989) 1–7 [pdf, pdf]

On domain theory internal to cartesian closed categories:

On star-autonomous categories and the Chu construction as categorical semantics for linear logic:

and via accessible categories:

On coalgebras for an endofunctor:

  • Michael Barr, Terminal coalgebras for endofunctors on sets, Theoretical Comp. Sci. 114 (1993) 299–315 [pdf, pdf]

On fuzzy logic

in relation to topos theory:

and in relation to linear logic:

On the HSP theorem:

On category theory in computer science, via star-autonomous categories and Chu spaces:

  • Michael Barr, Charles Wells, Category theory for computing science, Prentice-Hall International Series in Computer Science (1995); reprinted in: Reprints in Theory and Applications of Categories 22 (2012) 1-538 [pdf, tac:tr22]

On acyclic objects in categories of chain complexes:

On the Chu construction:

On the Chu construction on Vect:

On sketches:

  • Michael Barr, Notes on Sketches, Technical report of the Electrotechnical Laboratory (computer language section), Tsukuba, Japan (1997) [pdf, pdf]

On relational structures:

  • Michael Barr, Note on a theorem of Putnam’s, Theory Appl. Categories, 3 3 (1997) 45–49 [tac:3-03]

On the Chu construction and star-autonomous categories:

  • Michael Barr, The separated extensional Chu category Theory Appl. Categories 4 6 (1998) 127–137 [tac:4-06]

On star-autonomous categories of unit balls in Banach spaces:

More on star-autonomous categories:

  • Michael Barr, *\ast-Autonomous categories: once more around the track, Theory and Applications of Categories 6 1 (1999) 5-24 [tac:6-01]

On topological star-autonomous categories:

English translation of Alexander Grothendieck‘s Tohoku-article on homological algebra:

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.

On the Chu construction:

On product spaces with Lindelöf topological spaces:

On computability and formal languages:

On Isbell duality:

and specifically for modules:

On discrete dynamical systems (here called “flows”) on compact Hausdorff spaces:

On coherent spaces:

On injective hulls of partially ordered monoids:

On star-autonomous categories of sup-semilattices:

On limits of integral domains among commutative rings:

On limits of integral domains among commutative rings:

On reflective and coreflective subcategories:

On contractibility of simplicial objects:

On coequalizers and free monads:

category: people

Last revised on November 12, 2023 at 11:17:48. See the history of this page for a list of all contributions to it.