Categories for Grassmannian Cluster Algebras of Infinite Rank

Abstract We construct Grassmannian categories of infinite rank, providing an analogue the cluster introduced by Jensen, King, and Su. Each category rank is given as graded maximal Cohen–Macaulay modules over a certain hypersurface singularity. show that generically free $1$ in are bijection with Plücker coordinates appropriate algebra rank. Moreover, this structure preserving, it relates rigidity to compatibility coordinates. Along way, we develop combinatorial formula compute dimension $\textrm {Ext}^{1}$-spaces between any two