2016/06/03 by Scoville, Nicholas A., Swei, Willie
#06F30 #55M30 #55U05 #55U10 #Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1606.01205
In this paper, we study the Lusternik-Schnirelmann category of a simplicial map between simplicial complexes, generalizing the simplicial category of a complex to that of a map. Several properties of this new invariant are shown, including its relevance to products and fibrations. We relate this category of a map to the classical Lusternik-Schnirelmann category of a map between finite topological spaces. Finally, we show how the simplicial category of a map may be used to define and study a simplicial version of the essential category weight of J. Strom.