An approach to indexical beliefs is presented and defended in the paper. The account is inspired by David Kaplan’s representationalist analysis of de re belief reports. I argue that imposing additional constraints on the Kaplanian notion of representation results in an elegant theory of indexical beliefs. The theory is committed to representations of limited accessibility but is not committed to relativized proposition, special de se contents or propositions of limited accessibility.
The classical Serre-Swan's theorem defines an equivalence between the category of vector bundles and the category of finitely generated projective modules over the algebra of continuous functions on some compact Hausdorff topological space. We extend these results to obtain a correspondence between the category of representations of an étale Lie groupoid and the category of modules over its Hopf algebroid that are of finite type and of constant rank. Both of these constructions are functorially defined on the Morita category of étale Lie groupoids and we show that the given correspondence represents a natural equivalence between them.