Consistent pairs of $ \mathfrak{s} $-torsion pairs in extriangulated categories with negative first extensions

Abstract

<abstract><p>As a generalization of a consistent pair of $ t $-structures on triangulated categories, we introduced the notion of a consistent pair of $ \mathfrak{s} $-torsion pairs in the extriangulated setup. Let $ (\mathcal{T}_{i}, \mathcal{F}_{i}) $ be an $ \mathfrak{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 $ (\mathcal{T}_{1}\ast\mathcal{T}_{2}, \mathcal{F}_{1}\cap\mathcal{F}_{2}) $ to be an $ \mathfrak{s} $-torsion pair. Our results were then applied to the torsion theory induced by $ \tau $-rigid modules.</p></abstract>