The simplicial LS-category of a finite abstract simplicial complex is a new invariant of the strong homotopy type, defined in purely combinatorial terms. We prove that it generalizes to arbitrary simplicial complexes the well known notion of arboricity of a graph, and that it allows to develop many notions and results of algebraic topology which are costumary in the classical theory of Lusternik–Schnirelmann category. Also we compare the simplicial category of a complex with the LS-category of its geometric realization and we discuss the simplicial analogue of the Whitehead formulation of the LS-category.
"Simplicial Lusternik-Schnirelmann category." Publ. Mat. 63 (1) 265 - 293, 2019. https://doi.org/10.5565/PUBLMAT6311909