Abstract: The Healy-McInnes UMAP algorithm for a data set $X$ has been highly successful as a data science tool. The goal of this talk is to present a geometric version of this algorithm. The present approach requires Barr's generalized fuzzy sets with coefficients in the interval $[0,\infty]$, completeness properties of extended pseudo-metric spaces (ep-metric spaces), and manipulations of simplicial presheaves. We also use a geometric version of the cross entropy function for fuzzy sets with coefficients in $[0,\infty]$, which can be effectively bounded by distance.