Almost split triangles and morphisms determined by objects in extriangulated categories

Abstract Let ( C , E , s ) be an Ext-finite, Krull-Schmidt and k-linear extriangulated category with k a commutative artinian ring. We define an additive subcategory C r (respectively, C l ) of C in terms of the representable functors from the stable category of C modulo s -injectives (respectively, s -projectives) to k-modules, which consists of all s -projective (respectively, s -injective) objects and objects isomorphic to direct summands of finite direct sums of all third (respectively, first) terms of almost split s -triangles. We investigate the subcategories C r and C l in terms of morphisms determined by objects, and then give equivalent characterizations on the existence of almost split s -triangles.