How do I show that the category of sheaves on a space $X$ taking values in , a category $K$ admitting inverse limits, admits inverse limits?
The limit is a presheaf, I tried to show that it is also a sheaf but I cannot establish the existence of the morphisim from any given object $T$ in $K$ to $F(U)$ satisfying the definition of a sheaf (as in the stacks project for example).