Extensions of the categorical bijection to other poset classes

Establish versions of the canonical categorical isomorphism between strong formal subdivisions and join-admissible mapping-cylinder data for other interesting classes of posets beyond lower Eulerian and CW-posets.

Background

The paper proves a categorical correspondence between strong formal subdivisions of lower Eulerian posets and triples consisting of a lower Eulerian poset, a rank function, and a non-minimal join-admissible element. It also establishes an analogous result for CW-posets.

The authors explicitly ask whether analogous versions exist for other interesting classes of posets, indicating that the scope of the mapping-cylinder and join-admissibility correspondence remains unresolved beyond the classes treated in the paper.