Martin Escardo wrote:
NB. Freyd characterized the Dedekind reals as a final coalgebra. Alex Simpson and I characterized "the Cauchy completion of the rationals within the Dedekind reals" as a free algebra
and vaughan pratt and i characterized the cauchy reals as a final coalgebra. the papers are i proceedings of CMCS 99 and in TCS 280. in fact, freyd came up with his characterization of the closed interval while commenting on our first paper, where vaughan and i worked with the semiopen interval. but it is fair to say that the algebraic approach allows easier algebraic operations on reals. (i only managed to multiply them in one of our coalgebras, and in a very inefficient way.) -- dusko BTW have you seen the book: Life Itself. A Comprehensive Inquiry Into the Nature, Origin, and Fabrication of Life by Robert Rosen (Columbia University Press 1991) it was referenced in a biology paper, i found it in the biology library, and it's full of categories. (yes, i kno, people often do that to sound complicated, but this seems like honest work, perhaps even inspiring, although it does not go very deep.)