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AIDb
s

sheaf

Collection of objects associated to subsets of a space in a manner admitting gluing and restriction

EntityQ595298
Subclass of

All data

23 statements · 17% with external sources · numbers in brackets are citations

Studied by
Defining formula
  • \begin{align}&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\restriction U_i=t\restriction 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\restriction U_i\cap U_j=s_j\restriction U_i\cap U_j\implies\exists s\in F(U)\forall i\in I\colon s_i=s\restriction U_i\end{align}
Discovered by
Discovered
  • 1947
Has characteristic
Different from
Dual notion (category theory)

On other databases

12 identifiers linking sheaf across the web's reference databases