How do prime ideals relate number theory and algebraic geometry?
Presheaf - restrictions can be thought of as morphisms? associative?
Daping Weng. A Categorical Introduction to Sheaves I noticed that we can think of presheaves in terms of category theory, or more specifically, in terms of topological spaces with open sets. So I am curious how the topologically defined sheaves might be thought more generally in terms of category theory. I think this paper answers that question.
Algebraic geometry deals with crosssections (zeros) and considers values in various grids (natural numbers, integers, rationals, reals, complexes).
Resolution of singularities. For each projective variety X, there is a birational morphism W->X where W is smooth and projective. (This brings to mind universal covering spaces, the unfolding of loops into paths.)
Sheaf theory can be used to model perspectives. They impose a global context (question) (the type of data that we want such as a ring of continuous functions) upon the local domains (open sets) with regard to which the data (answer) is provided (the question is answered).