The standard "foundation" for mathematics starts with sets and their elements. It is possible to start differently, by axiomatising not elements of s…

- Saunders Mac Lane

... the notions category and functor were not formulated or put in print until the idea of a natural transformation was also at hand.

- Saunders Mac Lane

. . . in one sense a foundation is a security blanket: If you meticulously follow the rules laid down, no paradoxes or contradictions will arise. In …

- Saunders Mac Lane

. . . the membership relation for sets can often be replaced by the composition operation for functions. This leads to an alternative foundation for …

- Saunders Mac Lane