so what's an example of a sheaf (of abelian groups??? or something??) without a projective resolution?? ... or something ... ??

??what about case of coherent sheaves??? ... ??hmm, simply (??) something about way unit coherent sheaf isn't projective??? .... ???...

??what about example of non-coherent sheaf of modules ??? ... ??for example over affine line, if such exist??

what's this business about how existence of "generator" and injective resolutions (or something...) allegedly relates to subobject classifier?? ??and what's the history of this??