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In recent years philosophers of science have explored categorical equivalence as a promising criterion for when two (physical) theories are equivalent. On the one hand, philosophers have presented several examples of theories whose relationships seem to be clarified using these categorical methods. On the other hand, philosophers and logicians have studied the relationships, particularly in the first order case, between categorical equivalence and other notions of equivalence of theories, including definitional equivalence and generalized definitional (aka Morita) equivalence. In this article, I will express some skepticism about this approach, both on technical grounds and conceptual ones. I will argue that category structure (alone) likely does not capture the structure of a theory, and discuss some recent work in light of this claim.
In 1717 Halley compared contemporaneous measurements of the latitudes of four stars with earlier measurements by ancient Greek astronomers and by Brahe, and from the differences concluded that these four stars showed proper motion. An analysis with m
In this article we review how categorical equivalences are realized by renormalization group flow in physical realizations of stacks, derived categories, and derived schemes. We begin by reviewing the physical realization of sigma models on stacks, a
We provide a novel perspective on regularity as a property of representations of the Weyl algebra. In Part I, we critiqued a proposal by Halvorson [2004, Complementarity of representations in quantum mechanics, Studies in History and Philosophy of Mo
We provide a novel perspective on regularity as a property of representations of the Weyl algebra. We first critique a proposal by Halvorson [2004, Complementarity of representations in quantum mechanics, Studies in History and Philosophy of Modern P
I review the philosophical literature on the question of when two physical theories are equivalent. This includes a discussion of empirical equivalence, which is often taken to be necessary, and sometimes taken to be sufficient, for theoretical equiv