Extriangulated factorization systems, s -torsion pairs and recollements

Key Points

• The aim is to establish a connection between extriangulated factorization systems and s-torsion pairs.
• Introduced extriangulated factorization systems in extriangulated categories.
• Established a bijection between s-torsion pairs and extriangulated factorization systems.
• Examined gluing methods of s-torsion pairs and factorization systems through recollements.
• A clear bijection between s-torsion pairs and extriangulated factorization systems exists.
• The study advances understanding of how these systems interact under recollement operations.