The boundary between philosophical and logical foundational studies of mathematics is very unclear indeed – one has only to think of Russell’s part in Principia Mathematica. For a discussion of more obviously logical foundational aspects of category theory see foundations.
To be done
Jean-Pierre Marquis, 1995, Category Theory and the Foundations of Mathematics: Philosophical Excavations. Synthese 103 (3).
Colin McLarty, 2004, ‘Exploring Categorical Structuralism’, Philosophia Mathematica, 12, 37–53.