The Stanley-Reisner ring is defined for a simplicial complex, or a simplicial poset slight generally, in order to express the combinatorial structure algebraically, and it has been a central object in combinatorics since its introduction. A topological realization of the Stanley-Reisner ring due to Davis and Januszkiewics shows that the Stanley-Reisner ring is isomorphic with the limit of a certain functor.

In this talk, we will generalize this functor to an arbitrary poset and show its basic properties on higher limits and topological realization. This talk is based joint work with Ran Levi.