Topos Theory (Part 6)

I’m 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 tackled the first two bullet points; now let’s do the third. For starters, what’s a cartesian closed category, and why are they so nice? Answering this question will get us into some more ‘philosophical’ aspects of topos theory.

Cartesian closed categories

The category of sets has ‘sums’, also...