27 Nov
2005
27 Nov
'05
1:49 a.m.
Well, it does seem that "semigroupoids" is the preferred terminology. Searching on this term through the math xxx archive pulls up a number of papers which study various kinds of C star algebras built on top of semigroupoids. The idea is to use the objects of the semigroupoid to index a basis in a (separable) Hilbert space and to use the arrows to define partial isometries of this Hilbert space in the obvious way. The algebra closure in the weak operator topology then defines the "semigroupoid" C star algbera. Of course this algebra does contain one idempotent for each object, but this is a consequence of taking the algebra- closure of the set of patial isometries defined by the arrows. Carl Futia