 Building on these developments, the philosophical discussion of categorical structuralism was initiated by Awodey, Landry, Marquis, and McLarty in the 1990s.  To understand their contributions better, it helps to go back to our distinction between “metaphysical” and “methodological structuralism”, which is drawn explicitly in Awodey (1996).  Or rather, Awodey distinguishes between the use of category theory as a framework for “mathematical” and for “philosophical structuralism”. He describes mathematical structuralism as a general way of “pursuing a structural approach to the subject“, i.e., a particular style of practicing mathematics that employs structural concepts and methods.  He then argues that category theory provides the best way of capturing structural mathematics in this sense. However, he also presents it as a framework for philosophical structuralism, i.e., “an approach to the ontology and epistemology of mathematics”.  Let us first consider the former argument. (We will return to the latter in  section 3.3).