Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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
   • PermaLink
   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)
   • PermaLink
   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