Summary: An edge irregular total \(k\)-labeling of a graph \(G=(V,E)\) is a labeling \(f:V \cup E \rightarrow \{1,2,\dots ,k\}\) such that the total edge-weights \(wt(xy)=f(x)+f(xy)+f(y)\) are different for all pairs of distinct edges. The minimum \(k\) for which the graph \(G\) has an edge irregular total \(k\)-labeling is called the total edge irregularity strength of \(G\). In this paper, we determine the exact value of the total edge irregularity strength of the categorical product of two paths \(P_n\) and \(P_m\). Our result adds further support to a recent conjecture of J. Ivančo and S. Jendrol [Discuss. Math., Graph Theory 26, No. 3, 449–456 (2006; Zbl 1135.05066)].