Re: The Idea of Structure as Data and Conditions

[Staffan Angere <Staffan.Angere@fil.lu.se>]

I am not certain that is a good example, actually. The membership relation is certainly what gives the structure of a model of ZFC, so it may be relevant to morphisms between such models. However, it does not have to have anything to do with the structure of individual sets.

The structure of a single set is, I believe, most fruitfully thought of as just consisting of the identity relation on its elements. That way, the morphisms come out as functions (i.e. identity-preserving total relations), just as we expect them to.

Best wishes,
Staffan


________________________________________
Från: FEJ Linton [FLinton@Wesleyan.edu]
Skickat: den 28 maj 2012 08:00
Till: categories@mta.ca
Ämne: categories: Re: The Idea of Structure as Data and Conditions

On Sat, 26 May 2012 19:48:26 -0400 (EDT), Michael Barr wrote:

> Let me point out that not every structure comes with an obvious notion of
> morphism.  --- [examples snipped] ---

The most common example: sets. The structure is based on membership.
Virtually no one ever wants to restrict attention to functions that respect
(preserve or reflect) membership (other than "preserve" between ordinals).

Cheers, -- Fred



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