sheaf (Q2083): Difference between revisions

${\displaystyle {\begin{aligned}&F\colon {\rm {Open}}(X)^{\rm {op}}\to {\rm {Set}}\\&U=\bigcup _{i\in I}U_{i}\land s,t\in F(U)\land (\forall i\in I\colon s\upharpoonright U_{i}=t\upharpoonright U_{i})\implies s=t\\&U=\bigcup _{i\in I}U_{i}\land \forall i\in I\colon s_{i}\in F(U_{i})\land \forall i,j\in I\colon s_{i}\upharpoonright U_{i}\cap U_{j}=s_{j}\upharpoonright U_{i}\cap U_{j}\implies \exists s\in F(U)\forall i\in I\colon s_{i}=s\upharpoonright U_{i}\end{aligned}}}$