Dear Carlos
Hi. I'm interested in following the discussion of enriched categories and ``comma objects'' on the categories list, and particularly in what you just wrote. But...what is a ``comma category'' or more generally ``comma object''?
Comma categories are explained, for example, in Mac Lane's book "Categories for the working mathematician" Grad Texts in Math #5 (Springer). In a sense they are "lax pullbacks" defined when given two functors with the same codomain. Hence, just as we can carry over the notion of pullback in Set to any category, we can carry over, by representability, the notion of comma category from Cat to any 2-category (I call them comma objects in SLNM 420).
Also, was your PhD thesis published? I used the notion of differential graded category in a paper about vector bundles a while ago; then found out that Kapranov et al had a few earlier papers about it, but I didn't know that it came from even before that.
Exaggerating only slightly, the whole reason enriched category theory got going in the 60s was to deal with the example of differential graded categories: these are categories enriched in chain complexes (Eilenberg-Kelly "Closed categories" LaJolla 1965). As I understand it, that example prompted Sammy and Max to their joint work: they had each used DG-categories before. My thesis [0] was not published in full. For the published papers [2], [5] on the thesis, I took out the stuff on DG-categories. However, [25] uses the DG-category approach very strongly and gives new proofs of more general results (I had some of these at the time of my thesis but hadn't included them). The papers provide universal coefficients (or homotopy classification) theorems for diagrams of chain complexes. 0. PhD Thesis: Homotopy Classification of Filtered Complexes, University of Sydney, August 1968. 2. Projective diagrams of interlocking sequences, Illinois J. Math. 15 (1971) 429-441; MR43#4881. 5. Homotopy classification of filtered complexes, J. Australian Math. Soc. 15 (1973) 298-318; MR49#5135. 25. Homotopy classification by diagrams of interlocking sequences, Math. Colloquium University of Cape Town 13 (1984) 83-120; MR86i:55025. Best regards, Ross www.mpce.mq.edu.au/~street/