Consistent pairs of s-torsion pairs in extriangulated categories with negative first extensions

As a generalization of a consistent pair of t-structures on triangulated categories, we introduced the notion of a consistent pair of s-torsion pairs in the extriangulated setup. Let (T-i, F-i) be an s-torsion pair in an extriangulated category with a negative first extension for any i = 1, 2. By using the consistent pair, we gave a criterion for (T-1 * T-2, F-1 boolean AND F-2) to be an s-torsion pair. Our results were then applied to the torsion theory induced by tau-rigid modules.