The IFF References

References pertinent to the IFF are listed here. The two main reference works are the books Sets for Mathematics by Lawvere and Rosebrugh and Categories for the Working Mathematician by Mac Lane. The latter is a good standard text giving an introduction to category theory and the former gives an introduction to categorical set theory closely related to the philosophy of the IFF.

F. William Lawvere and Robert Rosebrugh. Sets for Mathematics. Cambridge University Press, 2003. ISBN: 0521804442.
“Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. For the first time in a text, this book uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms which express universal properties of sums, products, mapping sets, and natural number recursion. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geometry and analysis, are made explicit and taken as special axioms. Functor categories are introduced in order to model the variable sets used in geometry, and to illustrate the failure of the axiom of choice. An appendix provides an explicit introduction to necessary concepts from logic, and an extensive glossary provides a window to the mathematical landscape.”
Saunders Mac Lane. Categories for the Working Mathematician. Series: Graduate Texts in Mathematics, Vol. 5. Springer-Verlag, 1971. 2^nd edition, 1998. ISBN: 0387984038.
“Categories for the Working Mathematician provides an array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. The book then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterized by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions.”