On Einstein algebras and relativistic spacetimes

•We present the theory of Einstein algebras using the algebraic theory of manifolds as presented by Nestruev (2003).•We establish a sense in which general relativity is categorically dual to the theory of Einstein algebras.•We comment on how this result bears on debates concerning substantivalism and relationism.

In this paper, we examine the relationship between general relativity and the theory of Einstein algebras. We show that according to a formal criterion for theoretical equivalence recently proposed by Halvorson, 2012 and Halvorson, 2015 and Weatherall (2015a), the two are equivalent theories.