Exercise 7.52

Exercise 7.52#


The one point space has two open sets and could be represented ∅ → {1}. Based on Eq. 7.50 we assign \(Ω(∅) = \{∅\}\) and we assign \(Ω(\{1\}) = \{∅,\{1\}\}\).

The non-empty set is being mapped to a two object set we can see as the booleans. Therefore we can see any morphism between sheaves (a natural transformation) that targets this sheaf as a function to the booleans.