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1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeMar 31st 2016
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexJust saw this on the arXiv: [The Fermat functors](http://arxiv.org/abs/1603.09266). We don't seem to have an entry on "Fermat reals" and I don't recall having heard of them before. But this paper seems to be reaching for a context of cohesion for this different kind of infinitesimal, although on a quick glance through I can't tell whether the functors are adjoint.

   Just saw this on the arXiv: The Fermat functors. We don’t seem to have an entry on “Fermat reals” and I don’t recall having heard of them before. But this paper seems to be reaching for a context of cohesion for this different kind of infinitesimal, although on a quick glance through I can’t tell whether the functors are adjoint.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeApr 5th 2016
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   Author: Urs
   Format: MarkdownItexThanks for pointing this out. I have no time to look into it at the moment, but from the words being used it does sound as if there might be some alternative differential cohesion here. Need to come back to this later.

   Thanks for pointing this out. I have no time to look into it at the moment, but from the words being used it does sound as if there might be some alternative differential cohesion here. Need to come back to this later.

3. • CommentRowNumber3.
   • CommentAuthorNikolajK
   • CommentTimeApr 7th 2016
   • (edited Apr 7th 2016)
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   Author: NikolajK
   Format: MarkdownItexFrom the first paper on this*, which I guess is this guys superior, it sounds like a SDG'ish theory, but underlying classical logic (the difference is dedicated a page, p.285). I think, explcitly, his Fermat reals *R are a ring of polynomials over R, modulo what's invisible w.r.t. little oh-notation. He also says that the "adding infinitesimals" functor doesn't always preserve colimits and has no right adjoint. The cateogry of spaces *C^\infty is a quasi-topos. * http://arxiv.org/pdf/0907.1872.pdf

   From the first paper on this*, which I guess is this guys superior, it sounds like a SDG’ish theory, but underlying classical logic (the difference is dedicated a page, p.285). I think, explcitly, his Fermat reals *R are a ring of polynomials over R, modulo what’s invisible w.r.t. little oh-notation.

   He also says that the “adding infinitesimals” functor doesn’t always preserve colimits and has no right adjoint. The cateogry of spaces *C^\infty is a quasi-topos.

   * http://arxiv.org/pdf/0907.1872.pdf