Jonathan Mock Beck (∞-2006) was an American mathematician working in category theory and algebraic topology. He received his Phd from Columbia University in 1964 under the supervision of Samuel Eilenberg and with a thesis on monads, algebras and cohomology (reprint here). He is famous for having proved the monadicity theorem? for a pair of adjoint functors. He has showned that Grothendieck theory of descent is a formal consequence of the monadicity theorem. He has introduced the notion of distributivity law? in the theory of monads.
He has developped the homology theory of monads in collaboration with Michael Barr?:
Beck made important contributions to the theory of loop spaces and infinite loop spaces:
Beck, J.: On H-spaces and infinite loop spaces. Category Theory, Homology Theory and their Applications III, Springer-Verlag (1969) 139?153
Adams J.F.: Infinite loop spaces. Annals of Mathematics studies, Princeton University Press (1978).