Lectures on Etale Cohomology
《Lectures on Etale Cohomology》 · 第 64 页 · Section 9「Cohomology: Definition and the Basic Properties」，开篇定义
The functor $F\mapsto\Gamma(X,F):\operatorname{Sh}(X_{\mathrm{et}})\to\operatorname{Ab}$ is left exact, and we define $H^r(X_{\mathrm{et}},-)$ to be its $r$th right derived functor. Explicitly, for a sheaf $F$, choose an injective resolution $0\to F\to I^0\to I^1\to\cdots$; then $H^r(X_{\mathrm{et}},F)$ is the $r$th cohomology group of the complex $\Gamma(X,I^0)\to\Gamma(X,I^1)\to\cdots$.