A new University of New Mexico technical report is available on DSpace, ECE-TR-08-0010. It describes an experiment in cognitive psychology that tests a (mathematical) category-theoretic model of categorization by humans. The model is part of a comprehensive theoretical model of the declarative semantics of neural networks. The report can be obtained by going to DSpaceUNM, or directly to http://hdl.handle.net/1928/6724 . Questions and comments are welcome. Mike Healy Electrical and Computer Engineering University of New Mexico Albuquerque, NM USA Abstract Categorization and the judgement of similarity are fundamental in cognition. We propose that these and other activities are based upon an underlying structure of knowledge, or concept representation, in the brain. Further, we propose that this structure can be represented mathematically in a declarative form via category theory, the mathematical theory of structure. We test the resulting mathematical model in an experiment in which human subjects provide judgements of similarity for pairs of line drawings using a numerical scale to represent degrees of similarity. The resulting numerical similarities are compared with those derived from the category-theoretic model by comparing diagrams. The diagrams represent distributed concept structures underlying the line drawings. To compare with a more conventional analysis technique, we also compare the human judgements with those provided by a two-dimensional feature space model equipped with a distance metric for the line drawings. The results are equally favorable for both models. Because of this and the putative explanatory power of the category-theoretic model, we propose that this model is worthy of further exploration as a mathematical model for cognitive science. Keywords categorization, (mathematical) category, cognition, colimit, concept, diagram, feature, morphism, similarity, theory