This was a very nice exposition. Two notes which helped my understanding: 1. There appears to be a typo in the gluing axiom. The second half of the hypothesis

This was a very nice exposition. Two notes which helped my understanding: 1. There appears to be a typo in the gluing axiom. The second half of the hypothesis should read res^{U_i}_{U_i ∩ U_j}(s_i) = res^{U_j}_{U_i ∩ U_j}(s_j) i.e. the unions should be swapped for intersections. This is somewhat obvious if you've been paying attention to the definition of the restriction map and think about what the axiom is trying to accomplish, but tripped me up enough that I needed to check on Wikipedia to make sure I was following along correctly. 2. I'm not confident on this (since I've never successfully understood what a sheaf is before), but I think the sets Γ(V,F) need to be defined as something like an indicator function over the domain of entities (or perhaps a counting function for the number of such entities), so you would actually want to say something like "the support of Γ(V,F)={p}" rather than "Γ(V,F)={p}". Maybe the latter is a standard shorthand for the former when working with this sort of thing, but as a non-expert, it took me a bit of thinking to figure out what the map res^V_V' was actually supposed to concretely be (f.ex. say V' is a chunk that doesn't contain our player. If Γ(V,F)={p}, then what is res^V_V'(p)? More to the point, if V' has no entities and is thus {}, how to we construct functions with it as the co-domain?) Of course, I could be misunderstanding the example or notation completely, but I don't think that's the case.