Systematicity commonly means that having certain cognitive capacities entails having certain other cognitive capacities. Learning is a cognitive capacity central to cognitive science, but systematic learning of cognitive capacities---second-order systematicity---has received little investigation. We proposed associative learning as an instance of second-order systematicity that poses a paradox for classical theory, because this form of systematicity involves the kinds of associative constructions that were explicitly rejected by the classical explanation. In fact, both first and second-order forms of systematicity can be derived from the formal, category-theoretic concept of universal morphisms to address this problem. In this paper, we derived a model of systematic associative learning based on (co)recursion, which is another kind of universal construction. This result increases the extent to which category theory provides a foundation for cognitive architecture.