Sets, Categories and Types

This is a pointer to a very nice post by Mike Shulman, at the n-Category Cafe, on set theory, category theory and type theory: "From Set Theory to Type Theory".

Many interesting and thought-provoking ideas there, clarifying certain conceptual differences between how set theory thinks of sets ("material set theory") and how category theory does, in a more structural way ("structural set theory"), and how type theory (perhaps) brings this together.