From prestreams to streams

Last time, I had described two satisfactory models of topological spaces with a local direction of time: Marco Grandis’ d-spaces, and Sanjeevi Krishnan’s prestreams. The two kinds form categories that are related by an adjunction S ⊣ D, discovered by Emmanuel Haucourt. S. Krishnan’s purpose was really to talk about streams, not prestreams, and I will show how they emerge from the study of that adjunction. In other words, we will answer the following question partly: what makes the prestreams of the form S(X, dX) so special? Read the full post.