Specialized · a field of logic
Category Theory
Objects and arrows, toposes and type theory: an abstract language for structure, and an alternative foundation for mathematics.
- The problem
- Can mathematics be founded on structure and transformation (arrows) rather than on membership in sets?
- The turning point
- The Curry–Howard–Lambek correspondence: proofs, programs, and arrows in a cartesian-closed category are one and the same.
- An open question
- How far can ∞-categories and topos theory serve as the working foundation for everyday mathematics?
The Canon
- Categories for the Working Mathematician 1971
- Conceptual Mathematics
- Intuitionistic Type Theory 1984
To study it
- Category Theory
- Topoi: The Categorial Analysis of Logic