Most gratifying! That is just what I was looking for -- thanks! Richard On Mon, May 12, 2014, at 10:16 PM, Michal Przybylek wrote: Dear Richard, What you call "Isbell envelope'', was called by John Isbell "couple category". The construction is defined in the following paper: J. R. Isbell, "Normal completions of categories" Best, Michal On Mon, May 12, 2014 at 6:09 AM, Richard Garner <[1]richard.garner@mq.edu.au> wrote: Dear categorists, One of the more folklorish constructions in category theory is that of the Isbell envelope. The folklorishness, in this case, seems to be so severe that I cannot find mention made of it in any published article at all (though there are several to the related notion of Isbell conjugacy). I am writing, therefore, in the hope that this is only due to my own poor knowledge of the literature, and that some other reader of this list may be able to put me to rights. Richard [For admin and other information see: http://www.mta.ca/~cat-dist/ ]