  Radical ontic structural realism (ROSR) asserts an ontological commitment to
'free-standing' physical structures understood solely in terms of fundamental
relations, without any recourse to relata which stand in these relations. Bain
(2011) has recently defended ROSR against the common charge of incoherence by
arguing that a reformulation of fundamental physical theories in
category-theoretic terms (rather than the usual set-theoretic ones) offers a
coherent and precise articulation of the commitments accepted by ROSR. In this
essay, we argue that category theory does not offer a more hospitable
environment to ROSR than set theory. We also show that the application of
category-theoretic tools to topological quantum field theory and to algebraic
generalisations of general relativity do not warrant the claim that these
theories describe 'object-free' structures. We conclude that category theory
offers little if any comfort to ROSR.
