#4.16

stalk, direct limit. disjoint union modulo equivalence relation: x_i in F(Ui) and xj in F(Uj) are "equivalent" if there exists k bigger than i and j such that (through transition restriction map) their image in Uk are the same. (then [x_i]=[x_j]). In particular x equi to rho(x)

 sections of global sections F(X) are bijective to maps {O_x to F}

sheaf of finite type

understanding "generated by finitely many sections"

also implies that stalk is zero implies restricted to some open is zero

quasi coherent sheaves form an abelian subcategory of Mod(O_X)

 sheaf associated to module M

Mor(F_M,G)=Hom_R(M,G(X))

f^-1 is left adjoint to f_star, implying there exists a map f^-1f_star to id

inverse image functor

quasi-coherent sheaf

locally free implies quasi-coherent