Constructivist and Structuralist Foundations: Bishop's and Lawvere's Theories of Sets
arXiv:1201.6272
Abstract
Bishop's informal set theory is briefly discussed and compared to Lawvere's Elementary Theory of the Category of Sets (ETCS). We then present a constructive and predicative version of ETCS, whose standard model is based on the constructive type theory of Martin-Löf. The theory, CETCS, provides a structuralist foundation for constructive mathematics in the style of Bishop.
28 pages