\begin{definition}[Definition:Direct Image of Presheaf]
Let $\mathbf C$ be a category.
Let $T_1 = \struct {S_1, \tau_1}$ and $T_2 = \struct {S_2, \tau_2}$ be topological spaces.
Let $f : T_1 \to T_2$ be continuous.
Let $\FF$ be a $\mathbf C$-valued presheaf on $T_1$.
\end{definition}