Maps Between Representations of Clans

We give a description of the homomorphisms between representations of a clan (see Crawley-Boevey, J. London Math. Soc.40 (1989), 9–30), more or less as it was done by Krause (J. Algebra137 (1991), 186–194) for string-algebras. As a consequence of our findings we can establish the irreducibility of all maps which are expected to be so. This allows us, after defining a natural exact structure on the category of representations, to calculate in many situations Auslander–Reiten sequences like in the string-algebra case.