Dear Categorists, I wish to label the following notion of (for lack of a better term) "generalized subfunctor" of a functor H: J ---> C in a manner that is consistent with the categorical community. What I call a "generalized subfunctor" of F is a category D, a pair of functors F: C --->D and G: J ---> D, and a monic natural transformation m: G ---> FoH. My motivation is to formulate the notion of "generically creating a generalized subfunctor" to such a functor H. Is there some standard alternative to the overloaded term "generalized"? By the way, I am somewhat interested in the case where H sends certain J-spans to product diagrams in C, so sketch-theoretic ideas are certainly welcome. -- Best Regards, Bob McGrail **************************************************** By virtue knowledge **************************************************** Bard College Division of Natural Science and Mathematics P.O. Box 5000 Annandale-on-Hudson, NY 12504 (914)758-7265 mcgrail@bard.edu http://inside.bard.edu/~mcgrail