# Why isn't the use category theory for graph transformation more prominent?

On the surface, it would seem that category theory would be a very natural and useful mathematical tool to address the subject of graph transformation. Yet, early indications from online searches seem to indicate that it hasn't received much use in practice. The most cited work seems to point to Minas and Schneider in "Graph Transformation by Computational Category Theory".

This leads me to wonder why the "natural" semantics of morphisms in category theory and the $Grph$ category are not exploited more broadly for this purpose. After briefly surveying Minas and Schneirder's paper, I did not see it as a powerful and concise tool for graph transforms. The use of boolean matrix algebra seems nearly as powerful, more concise, and highly efficient computationally.

I'm curious to know if the utility of category theory for this purpose is known to be weak, since I was interested in possibly using it as a foundation for some work. I'm interested in learning your insight and/or experience on this topic.

• It's pretty unlikely that the utility of category theory for this purpose is known to be weak, simply because it's difficult to prove a negative. I've found that this kind of question is generally very difficult to answer satisfactorily, and such answers as exist often impinge on sociological as well as mathematical factors. Feb 7, 2015 at 19:55
• I don't really see how category can be used to "implement" actual transformations, aside from drawing actual graphs in terms of objects and morphisms, and drawing a morphism/functor from one to the other. Which is nice, intuitive, and elegant, but also verbose. Feb 7, 2015 at 22:56
• Hmm, categories are really just big directed graphs, why isn't graph theory more prominent in the study of category theory? Feb 7, 2015 at 23:06
• Well, categories are graphs with a "multiplication". Apr 7, 2015 at 23:25

• I generally agree, but might not the same argument be made for sets? Their treatment is not algebraic; at least not chiefly. Yet, $Set$ is a very common category. My interest in the use of category theory was to allow for meaningful morphisms between the function and structure of systems (defined mathematically). The function of a subsystem is often more easily described algebraically, however, its structure is often best described in graph-theoretical form, hence my interest in using category theory as the basis for both, and the transformation from one to the other. Thoughts?