## Sheaves of holomorphic functions

I can sense vaguely that the sheaf is a central definition in the (superficially) horrendously abstract language of modern mathematics. There really does seem to be quite a distance, between crudely speaking, pre-1950 math and post-1950 math in the mainstream in terms of the level of abstraction typically employed. It is my hope that I will eventually accustom myself to the latter instead of viewing it as a very much alien language. It is difficult though, and  there are in fact definitions which take quite me a while to grasp (by this, I mean be able to visualize it so clearly that feel like I won’t ever forget it), which is expected given how long it has taken historically to condense to certain definitions golden in hindsight. In the hope of a step forward in my goal to understand sheaves, I’ll write up the associated definitions in this post.

Path lifting lemma:    Let $p : \tilde{X} \to X$ be a covering projection and $\gamma : [0,1] \to X$ be a path such that for some $x_0 \in X$ and $\tilde{x} \in \tilde{X}$, Continue reading “Path lifting lemma and fundamental group of circle”