Hello, Two quick questions: a) It is well known that there is no vertical composition of dinatural transformations. How about horizontal composition? i.e. Given S,S':C^op x C---->B T,T':C^op x C ----> B^op U,U':B^op x B --->A \alpha: S--->S' dinat \alpha': T--->T' dinat and \beta: U--->U' dinat is there a \beta \circ (\alpha',\alpha) and is it dinat? It should be. But I can not seem to find the right definition. How about if we restrict to a nice category of moduals for a nice algebra over a nice field? Does that help? I was hoping that the category of small categories, functors and dinat transformations should be a graph-category (a category enriched over graphs) but am having a hard time finding what the composition is. Did someone write on these things? b) Also, I was wondering if anyone ever wrote about quasi-dinatural transformations. Those are dinats where the target category is a 2-category and the hexagon commutes up to a two cell. They show up in something I am working on. But they are very painful. Has anyone worked on such things? Any thoughts? All the best, Noson Yanofsky