From wikipedia entry on Sheaf Cohomology I have found the intriguing passage: 'The essential point is to fix a topological space X and think of cohomology as a functor from sheaves of abelian groups on X to abelian groups.' 

I have looked closely into Grothendieck's paper [Some aspects of homological algebra](https://pdfs.semanticscholar.org/456b/8412038b59a80f9165bded8e965d815b611c.pdf) (1955-1957) but require some help to further locate the inception of this view of Sheaf Cohomology in the Mathematical Literature. 

I'd very much appreciate if someone could point me to the point in the mathematical literature where Grothendieck introduces this idea of cohomology as functor of sheaves of abelian groups on X to abelian groups. Thanks!