21 Apr
2008
21 Apr
'08
7:04 p.m.
Fellow category theorists, I'm looking for a ref for the following result: Let C be a finite category. Then TFAE -- C has colimits for all small filtered (well, directed is probably better) diagrams. -- Idempotents split in C. This doesn't seem to be in Makkai-Paré or Adamek-Rosicky, but surely somebody must have observed this. Actually the result is a bit more general since idempotents split in *any* category that has filtered colimits. Thanks in advance, François Lamarche