. . . the membership relation for sets can often be replaced by the composition operation for functions. This leads to an alternative foundation for Mathematics upon categories -- specifically, on the category of all functions. Now much of Mathematics… — Saunders Mac Lane Copy Share Image
... 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 Copy Share Image
. . . the membership relation for sets can often be replaced by the composition operation for functions. This leads to an alternative foundation… — Saunders Mac Lane Copy Share Image
The standard "foundation" for mathematics starts with sets and their elements. It is possible to start differently, by axiomatising not elements of sets but… — Saunders Mac Lane Copy Share Image
. . . in one sense a foundation is a security blanket: If you meticulously follow the rules laid down, no paradoxes or contradictions… — Saunders Mac Lane Copy Share Image
