== Article needs streamlining == 

 The well-intended additions over the past 12 months have unfortunately rendered the article too long and lacking structure. In addition, there are still quite important omissions in the text. 
 My view is that a few improvements are needed to restore the article to B+ status. 
 * The Introduction comes too close to the formal definition, leading to undue repetition of material 
 * The examples in the introduction are too detailed: the verification of the axioms (which should come after the Formal Definition anyway) burdens the text too much 
 * The choice of examples in the introduction could be improved:  
 ** Being real-valued is irrelevant in the first example 
 ** The most common function sheaves from geometry (esp. smooth functions, holomorphic functions) should make an early appearance 
 ** Presheaves that fail to be sheaves should make an appearance early (bounded functions is a good choice) 
 ** The example on solutions of diff equations may be too specialised here (should be shorter / later if included). 
 ** Should include the sheaf of sections ofany vector bundle, not just the tangent bundle (vector fields). This is indeed the motivating example for sheaves! 
 * The detailed example of the constant sheaf on a two-point space is way too detailed. It uses an enormous amount of space for what is a tedious but entirely straightforward exercise. And the example itself is too trivial for treatment in an encyclopaedia article. 
 * Sheaves of abelian groups require an own section, with exact sequences discussed briefly and a pointer to Abelian categories 
 * Sheaves of modules over a sheaf of rings need some space; good place to mention that vector bundle = locally free sheaf (over whatever structure sheaf of ones geometric structures) - further discussion belongs elsewhere 
 * The section on sheaf cohomology is of appropriate length (short) but not balanced: while injective resolutions do not lead to manageable computations, by far the most common way of computing cohomology groups besides the Čech method is using other acyclic resolutions (de Rham cohomology, Dolbeault cohomology, singular cohomology!). Pointing instead to Borel-Bott-Weil theorem is out of place here.