Abstract
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).
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References
Mac Lane, S. [1992] The protean character of mathematics, pp. 3–12 in: Echeverria, J., Ibarra, A., and Mormann, T., (eds.), The Space of Mathematics, Berlin: de Gruyter.
Mac Lane, S. [1971] Categories for the Working Mathematician, New York: Springer Verlag.
Mac Lane, S. and Moerdijk, I., [1992] Sheaves in Geometry and Logic. A First Introduction to Topos Theory, New York: Springer Verlag.
McLarty, C. [1992] Elementary Categories, Elementary Topoi, Oxford, U.K.: Oxford University Press.
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© 1997 Springer Science+Business Media Dordrecht
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Mac Lane, S. (1997). Categorical Foundations of the Protean Character of Mathematics. In: Agazzi, E., Darvas, G. (eds) Philosophy of Mathematics Today. Episteme, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5690-5_7
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DOI: https://doi.org/10.1007/978-94-011-5690-5_7
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