categories: Re: categorical incunabula

[F W Lawvere <wlawvere@acsu.buffalo.edu>]

This summary of that exciting epoch will be useful.

A crucial omission is the Eilenberg-Zilber
1950 paper in the Annals (reviewed by H. Cartan). This introduction of the
category now called simplicial sets was quite crucial in the development
of category theory and its applications, for example the 1949 application
by Eilenberg  and Mac Lane in their discovery of the k-invariants.

The first lines of the paper emphasize that the points functor  is not
faithful . I like to cite this category when confronted by recalcitrant
logicians or "universal topologists" who insist that such categories are
"abstract"; " real mathematicians" have been using them routinely for over
fifty years. 



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F. William Lawvere			
Mathematics Department, State University of New York
244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA
Tel. 716-645-6284		   
HOMEPAGE:  http://www.acsu.buffalo.edu/~wlawvere
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