nLab Jon Beck

Jonathan Mock Beck (1935-2006) was a category theorist whose thesis (under the supervision of Sammy Eilenberg) and subsequent work with Mike Barr have been highly influential in the development of the subject.

• Wikipedia article

• MathGenealogy page

Selected writings

On monads (“triples”), algebras over monads and monadic cohomology:

• Jonathan M. Beck: Triples, algebras and cohomology, PhD thesis, Columbia University (1967), reprinted as: Reprints in Theory and Applications of Categories 2 (2003) 1-59 [tac:tr2, pdf]

Introducing the monadicity theorem:

• Jon Beck, untitled manuscript (1968) [pdf]

• Jonathan Mock Beck: The tripleableness theorem, Reprints in Theory and Applications of Categories 31 (2024) 1-11 [tac:tr31, pdf]

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

• H. Applegate, M. Barr, J. Beck, F. W. Lawvere, F. E. J. Linton, E. Manes, M. Tierney, F. Ulmer: Seminar on Triples and Categorical Homology Theory, ETH 1966/67, edited by Beno Eckmann and Myles Tierney, LNM 80, Springer (1969), reprinted as: Reprints in Theory and Applications of Categories 18 (2008) 1-303 [TAC:18, pdf]

Particularly on distributive laws:

• Jon Beck, Distributive Laws, in: Seminar on Triples and Categorical Homology Theory, ETH 1966/67, Lecture Notes in Mathemativs, Springer (1969), Reprints in Theory and Applications of Categories 18 (2008) 1-303 [TAC:18, pdf]

and on monadic cohomology via canonical resolutions:

• Michael Barr, Jon Beck, Homology and Standard Constructions, in: Seminar on Triples and Categorical Homology Theory, Lecture Notes in Maths. 80, Springer (1969), Reprints in Theory and Applications of Categories 18 (2008) 186-248 [TAC:18, pdf]

category: people