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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).

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    $\begingroup$ Limits commute with limits, so a limit of equalizers is an equalizer $\endgroup$ – Max Apr 1 at 6:51
  • $\begingroup$ Once you interpret a sheaf as an equalizer and then interpret an equalizer as a limit , this becomes a trivial fact. $\endgroup$ – Zee Apr 9 at 5:06

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