Dynamical combinatorics and torsion classes

For finite semidistributive lattices the map κ gives a bijection between sets of completely join-irreducible elements and meet-irreducible elements. Here we study -map in context torsion classes. It is well-known that lattice classes for an artin algebra semidistributive, but general it far from finite. We show well-defined on set elements, even when infinite. then extend to which have canonical join representations given by special associated minimal extending modules introduced first third authors A. Carroll 2019. hereditary algebras , extended essentially same as Ringel's ϵ wide subcategories . Also case, relate square Auslander-Reiten translation.