Categorical foundations of the protean character of mathematics
pp. 117-122
in: Evandro Agazzi, György Darvas (eds), Philosophy of mathematics today, Berlin, Springer, 1997Abstract
Mathematics is protean; it is that part of science which deals with "things," each of which can appear in many different applications. The "things" are often described as "structures". Despite the familiar emphasis on set-theory, these structures are more than just sets; thus a group G is a set such that any two elements g and h of the group G have a product gh with the usual good algebraic properties. A vector space V is a set of things (vectors) which can be suitably added and suitably multiplied by scalars (real numbers).