Lusternik–Schnirelmann category of relation matrices on finite spaces and simplicial complexes
This paper focuses on matrices associated with maps on finite spaces (posets) and simplicial complexes. A map between finite spaces (simplicial complexes) and its homotopy (contiguous) class can be classified by the associated matrix. As an application, we propose a combinatorial method for calculating the Lusternik–Schnirelmann category of a map on finite spaces. Categorical (contractible) subspaces can be distinguished by a fundamental operation on components of the associated matrix.