some economic applications of scott domains

The present paper is structured around two main constructions, fixed points of functors and fibrations and sections of functors. Fixed points of functors are utilized to resolve problems of infinite regress that have recently appeared in economics. Fibrations and sections are utilized to model solution concepts abstractly, so that we can solve equations whose arguments are solution concepts. Most of the objects (games, solution concepts) that we consider can be obtained as some kind of limit of their finite subobjects. Some of the constructions preserve computability. The paper relies heavily on recent work on the semantics of program- ming languages.scott domains,infinite regress,game theory

The homotopy fixed point spectra of profinite Galois extensions

Let E be a k-local profinite G-Galois extension of an E_infty-ring spectrum A (in the sense of Rognes). We show that E may be regarded as producing a discrete G-spectrum. Also, we prove that if E is a profaithful k-local profinite extension which satisfies certain extra conditions, then the forward direction of Rognes's Galois correspondence extends to the profinite setting. We show the function spectrum F_A((E^hH)_k, (E^hK)_k) is equivalent to the homotopy fixed point spectrum ((E[[G/H]])^hK)_k where H and K are closed subgroups of G. Applications to Morava E-theory are given, including showing that the homotopy fixed points defined by Devinatz and Hopkins for closed subgroups of the extended Morava stabilizer group agree with those defined with respect to a continuous action and in terms of the derived functor of fixed points.Comment: 60 Page

Pro-categories in homotopy theory

The goal of this paper is to prove an equivalence between the model categorical approach to pro-categories, as studied by Isaksen, Schlank and the first author, and the $\infty$-categorical approach, as developed by Lurie. Three applications of our main result are described. In the first application we use (a dual version of) our main result to give sufficient conditions on an $\omega$-combinatorial model category, which insure that its underlying $\infty$-category is $\omega$-presentable. In the second application we consider the pro-category of simplicial \'etale sheaves and use it to show that the topological realization of any Grothendieck topos coincides with the shape of the hyper-completion of the associated $\infty$-topos. In the third application we show that several model categories arising in profinite homotopy theory are indeed models for the $\infty$-category of profinite spaces. As a byproduct we obtain new Quillen equivalences between these models, and also obtain an example which settles negatively a question raised by Raptis