Gluing support τ-tilting modules via symmetric ladders of height 2

Gluing techniques with respect to a recollement have long been studied. Recently, ladders of recollements of abelian categories were introduced as important tools. In this paper, we present explicit constructions of gluing of support τ-tilting modules via symmetric ladders of height two. Moreover, we apply the result to triangular matrix algebras to give a detailed version of the known Jasso’s reduction and study maximal green sequences.