Almost split sequences in a functor category (Q1112157)

Let k be a field, \(\Lambda\) a finite dimensional k-algebra, mod \(\Lambda\) the category of finite dimensional left \(\Lambda\)-modules and m-mod \(\Lambda\) the category of finitely presented k-linear functors mod \(\Lambda\) \(\to mod k.\) The author gives an explicit construction of almost split sequences (a.s.s.) in m-mod \(\Lambda\). For a non-projective indecomposable functor this construction parallels that of P. Gabriel for mod \(\Lambda\). It is also explained how to derive some a.s.s. in m-mod \(\Lambda\) from a.s.s. in mod \(\Lambda\), thus connecting the Auslander-Reiten quivers of m-mod \(\Lambda\) and mod \(\Lambda\). Finally the author gives some remarks on projective and injective presentations in m-mod \(\Lambda\).