A category theory perspective on compositionality and (the development of) cognitive capacity

A remarkable property of human cognition is the systematic co-occurrence of certain cognitive abilities. One challenge for cognitive science is to determine the (computational) principles that derive this property as part of a broader goal of establishing the foundations of cognitive architecture (i.e. the basic processes and modes of combination affording cognitive capacity) for a science of cognition. This paper continues a category theory approach to compositionality and cognitive capacity that posits universal construction (e.g., products) as a fundamental cognitive architectural component. As shown here, products can be modeled in other frameworks, thereby providing a link between an abstract computational principle and a concrete cognitive resource needed for particular capacities. For example, a network of weighted connections implementing a categorical product uses fewer resources when the number of task instances sharing a common product structure is greater than two; otherwise it is more economic to realize each instance independently. This cross-over may explain why human cognition is not always systematic: the cost of universal construction may not outweigh its expected gain.