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1. • CommentRowNumber1.
   • CommentAuthorjoe.hannon
   • CommentTimeFeb 28th 2013
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   Author: joe.hannon
   Format: MarkdownItexIn the article on [global sections](http://ncatlab.org/nlab/show/global+section), global sections are defined as the hom-set from the terminal object in the category of sheaves on a space $X$. This terminal object is also denoted $X$. But what is the terminal object in the category of sheaves? I would guess it should be the constant sheaf at the terminal object of target category: $*(U)=*$ for all $U\subseteq X.$ Is that not correct? Because I don't understand the notation $X$ for this sheaf.

   In the article on global sections, global sections are defined as the hom-set from the terminal object in the category of sheaves on a space $X$. This terminal object is also denoted $X$. But what is the terminal object in the category of sheaves? I would guess it should be the constant sheaf at the terminal object of target category: $*(U)=*$ for all $U\subseteq X.$ Is that not correct? Because I don’t understand the notation $X$ for this sheaf.

2. • CommentRowNumber2.
   • CommentAuthorZhen Lin
   • CommentTimeFeb 28th 2013
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   Author: Zhen Lin
   Format: MarkdownItexLet $X$ be a space. Then the terminal sheaf is precisely the sheaf of sections of $id : X \to X$ considered as a fibre bundle over $X$.

   Let $X$ be a space. Then the terminal sheaf is precisely the sheaf of sections of $id : X \to X$ considered as a fibre bundle over $X$.

3. • CommentRowNumber3.
   • CommentAuthorjoe.hannon
   • CommentTimeFeb 28th 2013
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   Author: joe.hannon
   Format: MarkdownItexI see. A section of the identity is the identity. Hence $X(U)=\{\text{id}_U\}$, and since each set of sections is a singleton, we do have the sheaf as a constant functor to the terminal object, as expected. Thank you for explaining.

   I see. A section of the identity is the identity. Hence $X(U)=\{\text{id}_U\}$, and since each set of sections is a singleton, we do have the sheaf as a constant functor to the terminal object, as expected. Thank you for explaining.