ABSTRACT
Ladder functors were introduced in [14] and [16] as a tool for the structural analysis of categories A with Auslander-Reiten sequences. The original idea of a ladder goes back to Igusa and Todorov [6] who considered chains of maps
· · · −→ a0 λ0−→ a1 λ1−→ a2 −→ · · · between two-termed complexes ai such that the mapping cone of each λi is an almost split sequence. Being rare objects, such ladders were difficult to handle, but Igusa and Todorov successfully applied them to obtain their characterization of the Auslander-Reiten quivers of representation-finite artinian algebras. The corresponding problem in dimension one, i. e. for orders over a complete discrete valuation domain, was solved 15 years later by Iyama [8], who showed that (modified) ladders of arbitrary length are obtained when the starting morphism a0 ∈ A is special, i. e. if its isomorphism class is invariant modulo Rad2A. For this improvement, it has to be payed in return that at each step an of the ladder, trivial direct summands 0→ A have to be discarded before passing to an+1.
