Does anyone know a reference for the embedding of a cartesian closed category in a topos? I have a memory there is a general result of this kind. Many thanks Ronnie -- Prof R. Brown, School of Informatics, Mathematics Division, University of Wales, Bangor Dean St., Bangor, Gwynedd LL57 1UT, United Kingdom Tel. direct:+44 1248 382474|office: 382681 fax: +44 1248 361429 World Wide Web: home page: http://www.bangor.ac.uk/~mas010/ (Links to survey articles: Higher dimensional group theory Groupoids and crossed objects in algebraic topology) Symbolic Sculpture and Mathematics: http://www.cpm.informatics.bangor.ac.uk/sculmath/ Centre for the Popularisation of Mathematics http://www.cpm.informatics.bangor.ac.uk/ Raising Public Awareness of Mathematics http://www.cpm.informatics.bangor.ac.uk/rpamath/ 10-Jul-2001 20:08:05 -0300,1732;000000000001-00000016
Ronnie asks: Does anyone know a reference for the embedding of a cartesian closed category in a topos? I have a memory there is a general result of this kind. The standard Yoneda embedding of a small CCC into its category of presheaves preserves the CCC structure. 11-Jul-2001 09:38:36 -0300,2255;000000000000-00000018
Mw question was too imprecise. I really want to know if the cartesian closed category of compactly generated topological spaces can for general reasons be embedded in a topos, so I am asking if a large cartesian closed category can be embedded in a topos. Ronnie ----- Original Message ----- From: Robert A.G. Seely <rags@math.mcgill.ca> To: <r.brown@bangor.ac.uk> Sent: Tuesday, July 10, 2001 6:12 PM Subject: Re: Categories: Embedability
Do you mean "other than Yoneda"? I think Dana Scott was the first to publish what must have been folklore that Yoneda does actually preserve the Cartesian closed category structure in that case - I think he mentioned this in one of his CS papers in the early 70's.
- all the best, Robert
================== R.A.G. Seely <rags@math.mcgill.ca> <http://www.math.mcgill.ca/rags>
10-Jul-2001 20:08:09 -0300,814;000000000001-00000017
participants (3)
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Peter Freyd -
Ronald Brown -
Ronnie Brown