Sheaves and streams I: sheaves of locally monotone maps

Sheaves are a fundamental notion. In this post and later posts, I would like to explain some of the basic theory of the most mundane notion of sheaves: sheaves of sets over a topological space. My real goal is really to explore what sheaf technology can bring us in the study of streams and prestreams. To start with, I will introduce the classical notion of the étale space of a presheaf, and illustrate that on sheaves of locally monotone (resp., and continuous) maps on streams, and particularly in the case of the directed circle. Read the full post.