Dear List Members, two days ago I posted a message asking whether there is a formal definition of parsimony for fundamental scientific theories, perhaps using category theory. Here is a short summary of answers I received: Ralph Wojtowicz recommended to have a look at Part D in Volume II of Johnstone's "Sketches of an Elephant", which as he wrote contains discussions of constructions involving translations between formal systems and their semantic categories. As an example for parsimony in category theory, Eduardo Ochs suggested the have a look at the relationships between set theory, local set theories, and elementary toposes. The paper by F. Wiedijk, "Is ZF a hack? Comparing the complexity of some (formalist interpretations of) foundational systems for mathematics", Journal of Applied Logic 4, 622-645, 2006 ps.gz pdf dvi via http://www.cs.ru.nl/~freek/pubs/index.html also was recommended. Many thanks to all respondents and also to Vaughan Pratt for his refreshing critical remarks! The answer to the question appears to be more difficult than I had expected. As often in philosophy, this may be to a good extent due to difficulties in explaining what the question is. One important point which I failed to clarify is the difference between fundamental mathematical theories and fundamental scientific theories. Fundamental scientific theories may, I think, assume the fundamental mathematical theory to be given. They should not describe all possible structures but, on the contrary, pick from the mathematically given structures those that are physically realized. This difference might also put the problem of parsimony for scientific theories into a different light. But I'm not sure, of course. So long, Axel