Categorification of the Catalan monoid. (Q467523)

Let \(N_n=\{1,2,\ldots,n\}\) be the linearly ordered graph (quiver); \(\mathcal C_n\) the monoid of all order-decreasing and order-preserving full transformations of \(N_n\). It has been shown that there is a weak functorial action of \(\mathcal C_n\) on the category of modules over the path algebra of \(N_{n-1}\). Here this is put into general context of algebraic categorification and constructed a finitary additive 2-category whose Grothendieck ring is isomorphic to the semigroup algebra of the monoid \(\mathcal C_n\). The paper is very dense, instead of definitions are presented only links to other papers.