From sets to types, to categories, to sets
pp. 113-125
in: Giovanni Sommaruga (ed), Foundational theories of classical and constructive mathematics, Berlin, Springer, 2011Abstract
Three different styles of foundations of mathematics are now commonplace: set theory, type theory, and category theory. How do they relate, and how do they differ? What advantages and disadvantages does each one have over the others? We pursue these questions by considering interpretations of each system into the others and examining the preservation and loss of mathematical content thereby.