Talk:Characterization of Metacategory via Equations

Work on this page and Definition:Dual Statement (Category Theory) is to be continued; it needs to be cast into a proper form later on, when Definition:Language of Category Theory is up. I have, however, been trying to find a way to formally introduce a metacategory axiomatically. When the language page is up, the cod,dom,id and circ (and in fact $\mathbf C_0$ and $\mathbf C_1$, but they will be derived) will refer to the undefined terms of LCT. When I find a couple of hours of continuous free time I will make a dash at defining LCT, from which the appropriate ref's will be laid out. --Lord_Farin (talk) 21:23, 14 September 2012 (UTC)

The biggest problem here is that none of my references (not even MacLane, which is the most detailed on foundations) go this far into the formal logic part of foundations. Therefore, I am mostly on my own and have to tread with utmost caution. Even most of the theorems put up until now have been carefully generalised from the context of Awodey. --Lord_Farin (talk) 21:26, 14 September 2012 (UTC)

Trouble is, the field is still too new to have crystallised, so the definitions haven't been properly established. Once I get my current task out of the way I'll make the effort to penetrate 1964: Peter Freyd: Abelian Categories which talks covers this field. --prime mover (talk) 22:03, 14 September 2012 (UTC)