The term commonly used for the corresponding concept to lluf for groupoids is `wide'. I won't give a preference! `Representative subgroupoid' is used as for categories. Both occur in my 1968 book on topology, and I seem to remember the term wide was new. Ronnie Brown Charles Wells wrote:
"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
-- Professor Emeritus R. Brown, School of Informatics, Mathematics Division, University of Wales, Bangor Dean St., Bangor, Gwynedd LL57 1UT, United Kingdom Tel. direct:+44 1248 382474|office: 382681 fax: +44 1248 361429 World Wide Web: home page: http://www.bangor.ac.uk/~mas010/ (Links to survey articles: Higher dimensional group theory Groupoids and crossed objects in algebraic topology) Raising Public Awareness of Mathematics CDRom Version 1.1 http://www.bangor.ac.uk/~mas010/CDadvert.html Symbolic Sculpture and Mathematics: http://www.cpm.informatics.bangor.ac.uk/sculmath/ Centre for the Popularisation of Mathematics http://www.cpm.informatics.bangor.ac.uk/ 12-Jan-2002 09:15:25 -0400,2707;000000000000-00000000