Abstract
The article provides a mathematical categorical model characterisingthe relations that define the didactic object of second-ordercovariation from an epistemological perspective. The tools ofcategory theory make it possible to systematise the elaboration fromfirst-order covariation to second-order covariation in a unifiedtheoretical framework, including the intermediate transitionalphase, a topic that so far has not been explored in depth in theliterature. The unifying core of this process is the analysis of thenotion of adjunction of exponentials, and the context in which thisoccurs is provided by the Yoneda lemma. The various epistemic stepsof the dynamic categorical definition of second-order covariation areillustrated with reference to three classroom episodes.