Topos Theory (Part 7)

I’m almost done explaining why any presheaf category is an elementary topos, meaning that

• it has finite colimits;
• it has finite limits;
• it’s cartesian closed.
• it has a subboject classifier.

Last time I explained why such categories are cartesian closed; now let’s talk about the subobject classifier!

Subobject classifiers

In the category of sets, 0-element and 1-element sets play special roles. The 0-element set is the initial object, and any 1-element set is a terminal object. But...