The stalk of a sheaf at a point is just its stalk as a presheaf — the same defini- tion applies — and similarly for the germs of a section of a sheaf.
2026-04-04 04:37:32.1775277452
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what does the following statement mean?(sheaf and presheaf)
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The stalk of a presheaf $F$ is defined to be at a point $p$ is $$F_p= \lim_\rightarrow F(U)$$ where $U$ ranges over the all the subsets containing $p$ and the direct limit homomorphisms are simply the restriction maps from the presheaf structure. The sentence is saying that when asking about the stalks of a sheaf it has the exact same definition, as all sheaves are presheaves. A germ of a section $s$ its natural image in the direct limit, and again whether we are talking about sheaves or presheaves the same definition holds.
A sheaf is a presheaf with extra (gluing) conditions. Since any sheaf is also a presheaf, any definition one makes with a presheaf also applies to a sheaf.