What is category theory to cognitive science? Compositional representation and comparison

Category theorists and cognitive scientists study the structural (analogical) relations between domains of interest albeit in different contexts, that is, formal and psychological systems, respectively. Despite this basic commonality, very few cognitive scientists take a category theory approach toward understanding the structure of cognition which raises the question, What is category theory to cognitive science? An answer is given as the slogan “Category theory is to cognitive science as functor is to representation; as natural transformation is to comparison” to make category theory more accessible and informative for cognitive scientists.