Dear CT Community, I am new to Topos theory. Is it true that Hom[1->omega] in a topos defines a Heyting algebra? If so, please give me a reference where this is proved. Thanks and regards, Bill Halchin 22-Aug-2002 19:50:49 -0300,874;000000000000-00000000
On Wed, 21 Aug 2002, Galchin Vasili wrote:
Dear CT Community,
I am new to Topos theory. Is it true that Hom[1->omega] in a topos defines a Heyting algebra?
Yes
If so, please give me a reference where this is proved.
In almost any book on the subject: e.g. 5.13 in my own "Topos Theory", Theorem 5.6.4 in "Toposes, Triples and Theories" by Barr and Wells, Theorem IV 8.1 in "Sheaves in Geometry and Logic" by Mac Lane and Moerdijk, and Lemma A1.6.3 in "Sketches of an Elephant". Peter Johnstone 23-Aug-2002 16:18:15 -0300,2285;000000000001-00000000
Galchin Vasili wrote:
Dear CT Community,
I am new to Topos theory. Is it true that Hom[1->omega] in a topos defines a Heyting algebra? If so, please give me a reference where this is proved.
Thanks and regards, Bill Halchin
You will find this in MacLane and Moerdijk, Sheaves in Geometry and Logic. Check the index for "heyting algebras: of subobjects". I have the first printing of the first edition in which this result is Proposition 1 of the 8th section of chapter III. I believe this result can also be found in Lambek and Scott as well as Borceaux. Hope this helps. Bob McGrail Assistant Professor of Computer Science Bard College Annandale-on-Hudson, NY 12504 23-Aug-2002 16:27:21 -0300,935;000000000000-00000000
participants (3)
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Dr. P.T. Johnstone -
Galchin Vasili -
Robert McGrail