Beck's theorem

Last updated March 13, 2019

Beck's theorem may refer to either of two mathematical results:

Beck's monadicity theorem or the Beck tripleability theorem (1964/2003), by Jonathan Mock Beck, on monadic functors in category theory
Beck's theorem (geometry) (1983) by József Beck, on finite collections of points in discrete geometry

In category theory, a branch of mathematics, Beck's monadicity theorem gives a criterion that characterises monadic functors, introduced by Beck (2003) in about 1964. It is often stated in dual form for comonads. It is sometimes called the Beck tripleability theorem because of the older term triple for a monad.

In discrete geometry, Beck's theorem is any of several different results, two of which are given below. Both appeared, alongside several other important theorems, in a well-known paper by József Beck. The two results described below primarily concern lower bounds on the number of lines determined by a set of points in the plane.

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