DEGENERATION-LIKE ORDERS IN TRIANGULATED CATEGORIES

In an earlier paper we defined a relation <=(Delta) between objects of the derived category of bounded complexes of modules over a finite dimensional algebra over an algebraically closed field. This relation was shown to be equivalent to the topologically defined degeneration order in a certain space comproj (A, (d) under bar) for derived categories. This space was defined as a natural generalization of varieties for modules. We remark that this relation <=(Delta) is defined for any triangulated category and show that under some finiteness assumptions on the triangulated category <=(Delta) is always a partial order.