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 systematic-
ity 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 uni-
versal 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 pro-
vides a foundation for cognitive architecture.