T HE A UTONOMOUS S YSTEMS L ABORATORY UNIVERSIDAD POLIT ´ ECNICA DE MADRID Modeling cognitive systems with Category Theory Towards rigor in cognitive sciences Jaime G ´ omez and Ricardo Sanz ASLab A-2009-014 v 1.0 Final June 3, 2009 Contents 1 Introduction 2 2 The impasse of modelling the brain. Two obstacles and one way out 3 3 Category Theory 4 4 Applications of Category Theory in Cognitive Systems modeling 4 5 Category Theory for Perception 5 6 Category Theory for Consciousness 5 7 Conclusions 6 Abstract Traditionally, mathematical formalisms in cognitive sciences have been confined to toy model world descriptions. (5) 1