Beck's theorem

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In mathematics, there are two (different) theorems (by two different mathematicians) which go under the name of Beck's theorem.

  • In category theory, Beck's monadicity theorem (also known as the Beck tripleability theorem), proven by J. M. Beck around 1967, gives necessary and sufficient conditions for a functor to be monadic.
  • In incidence geometry, Beck's theorem (geometry) is a more quantitative form of the more classical Sylvester–Gallai theorem. It says that finite collections of points fall into one of two extremes; one where a large fraction of points lie on a single line, and one where a large number of lines are needed to connect all the points.