The Monoid Of Binary Relations On A Set Of Size Four Has Infinite Representation Type

The problem of determining the representation type of the full transformation monoid was resolved by Ponizovskii, Putcha, and Ringel. In this paper, we present a similar result for the monoid of binary relations, a partial result for the monoid of $\mathrm{\Lambda }$-generalized correspondences, and a sufficient condition for a monoid to have infinite representation type.