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(pointed out the notion of pointless toposes)

Revision as of 02:06, 14 February 2009

There is a notion of "pointless" toposes. It seems to me that "pointfree" is related to this idea. Some explanation follows.

A topos is thought of as a model for set theory. Hence it is natural to calculate with "elements". A topos is also a model for sheaves on a space. In that case it is natural to calculate with "stalks". In either case, we associate (functorially) to each object of our category a set "made up of elements" and then do the calculation with these elements. There are "pointless" toposes (for example the Deligne-Barr topos) so one should learn to carry out topos theoretic calculations with the crutch of "elements" or "points".

kapil 02:06, 14 February 2009 (UTC)