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1. • CommentRowNumber1.
   • CommentAuthorDmitri Pavlov
   • CommentTimeMar 30th 2013
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownThere seems to be a problem with the article [[infinitesimal object]]. The definitions of the infinitesimal k-cube D^k and the k-dimensional infinitesimal interval D(k) seem to be identical, modulo the fact that the latter seems to have several typos (specifically, the letters k and n are confused in several places). If my understanding is correct, the algebra of functions on D^k is the k-fold tensor product of the algebra of functions on D, which is k[x]/(x^2), thus the k-fold tensor product is k[x_1,…,x_k]/(x_1^2,…,x_k^2), which is much bigger than the current definition. The map from D(k) to D^k should then be given by modding out the ideal (x_i x_j) for i≠j.

   There seems to be a problem with the article infinitesimal object. The definitions of the infinitesimal k-cube D^k and the k-dimensional infinitesimal interval D(k) seem to be identical, modulo the fact that the latter seems to have several typos (specifically, the letters k and n are confused in several places).

   If my understanding is correct, the algebra of functions on D^k is the k-fold tensor product of the algebra of functions on D, which is k[x]/(x^2), thus the k-fold tensor product is k[x_1,…,x_k]/(x_1^2,…,x_k^2), which is much bigger than the current definition.

   The map from D(k) to D^k should then be given by modding out the ideal (x_i x_j) for i≠j.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMar 30th 2013
   • (edited Mar 30th 2013)
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   Author: Urs
   Format: MarkdownItexThanks for catching that, that was a bit of nonsense, indeed, not sure what happened there. The whole entry badly needs some attention. I had 5 minutes to edit. Have to interrupt now. Also removed this old query box, maybe Zoran could see if he remembers what he wanted to put into the entry here: +--{.query} Zoran: reason, if my memory is right, Leites in his around 1976 survey of supermanifolds proveds and puts important role of Hadamard's lemma in supercontext, but I do not recall details, maybe somebody shoudl check. =--

   Thanks for catching that, that was a bit of nonsense, indeed, not sure what happened there. The whole entry badly needs some attention.

   I had 5 minutes to edit. Have to interrupt now.

   Also removed this old query box, maybe Zoran could see if he remembers what he wanted to put into the entry here:

   +–{.query} Zoran: reason, if my memory is right, Leites in his around 1976 survey of supermanifolds proveds and puts important role of Hadamard’s lemma in supercontext, but I do not recall details, maybe somebody shoudl check. =–