Topos Theory: Subobject Classifier

Mode

Ω = {false, true}
true: 1 → Ω

In the topos Set, the subobject classifier Ω = {⊥,⊤}. Every subset S ⊆ A corresponds to a unique characteristic function χ_S: A → Ω sending elements of S to ⊤ and the rest to ⊥.

Interactive: Set A = {1,2,3,4,5}

Click elements to toggle subset S:

Topos Theory — Subobject Classifiers

Mode

Interactive: Set A = {1,2,3,4,5}