Categories in Context: Historical, Foundational, and Philosophical

Abstract

The aim of this paper is to put into context the historical, foundational and philosophical significance of category theory. We use our historical investigation to inform the various category-theoretic foundational debates and to point to some common elements found among those who advocate adopting a foundational stance. We then use these elements to argue for the philosophical position that category theory provides a framework for an algebraic in re interpretation of mathematical structuralism. In each context, what we aim to show is that, whatever the significance of category theory, it need not rely upon any set-theoretic underpinning.