Presheaf

Let $X$ be a topological space. A presheaf of sets $F$ on $X$ consist of the following data:

• A set $F(U)$ for every open $U\subseteq X$. It is usually denoted by $\Gamma(U,F)$. The elements are called sections. And $F(X)$ are called global sections.

• For each inclusion $U\subseteq V$ we have the so called restriction morphism

Often, for $s\in F(V)$ it is denoted $s|U=\mbox{res}_{ U,V}$(s)

• For every open set $U$, $\mbox{res}_{U,U}=id$

• Given three open sets $U\subseteq V\subseteq W$, $\mbox{res}_{U,V}\circ \mbox{res}_{V,W}=\mbox{res}_{U,W}$

They give rise to sheafs.

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Author of the notes: Antonio J. Pan-Collantes

antonio.pan@uca.es