My understanding of this ancient terminology ids that a replete subcategory is one that is closed under the forming of isomorphic copies.A subcategory which contains an isomorphic copy of every object in the containing category is called skeletal A subcategory ois both replete and skeletal if and only if it contains all objects of the larger category. ---John On 9/22/09 3:04 AM, "Fred Linton" <flinton@wesleyan.edu> wrote: Jim Stasheff asked,
What do you call it when you have one (small) category being a (full) subcategory of another, and every object in the big category is isomorphic to one in the small category ? ...
One adjective that *had* been used for such a subcategory (whether small, or full, or not) was "replete". I'll defer to others on the question of whether that terminology is still in use today, or is ... um ... *deprecated* :-) . Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]