"Lluf" is "full" written backward. Full means if the subcategory has two objects it has all the arrows between them. Lluf means the subcategory has all the objects of the containing category but not necessary all the arrows. Lluf is not a categorical notion. The more useful notion is REPRESENTATIVE subcategory. D is a representative subcategory of C if every object of C is isomorphic to an object of D. I think some writers have used "extensive" for "representative" but I don't have a reference. I don't know the history of those words. Charles Wells, Emeritus Professor of Mathematics, Case Western Reserve University Affiliate Scholar, Oberlin College Send all mail to: 105 South Cedar St., Oberlin, Ohio 44074, USA. email: charles@freude.com. home phone: 440 774 1926. professional website: http://www.cwru.edu/artsci/math/wells/home.html personal website: http://www.oberlin.net/~cwells/index.html genealogical website: http://familytreemaker.genealogy.com/users/w/e/l/Charles-Wells/ NE Ohio Sacred Harp website: http://www.oberlin.net/~cwells/sh.htm 12-Jan-2002 09:09:03 -0400,2950;000000000000-00000000