Topos Theory (Part 8)

Let’s look at an example of a presheaf topos, to see what various things I’ve been talking about actually look like—especially the subobject classifier.

Our example will illustrate the connection between topos theory and intuitionistic logic: that is, logic where the law of excluded middle, “p or not p”, fails. Intuitionistic logic goes back to Brouwer, who happens to have been born this very day in 1881. Topos theory formalizes intuitionistic logic in a way he might not have liked. But it...