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 k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum 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 sheaves 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.
   • CommentAuthorUrs
   • CommentTimeMay 11th 2010
   • (edited May 11th 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a section <a href="http://ncatlab.org/nlab/show/infinitesimal+object#SpacOfInfSimpl">Spaces of infinitesimal simplices</a>

   added a section Spaces of infinitesimal simplices

2. • CommentRowNumber2.
   • CommentAuthorEric
   • CommentTimeMay 11th 2010
   • PermaLink
   Author: Eric
   Format: MarkdownItexFYI: If you have a typo in the subject of a post, you can change it by editing the original comment.

   FYI: If you have a typo in the subject of a post, you can change it by editing the original comment.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 11th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks, Eric! I didn't know that, but did wonder about it. Good, so I fixed the typo.

   Thanks, Eric! I didn’t know that, but did wonder about it. Good, so I fixed the typo.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeMay 11th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexI am now pretty much through with completing and polishing that section on <a href="http://ncatlab.org/nlab/show/infinitesimal+object#SpacOfInfSimpl">Spaces of infinitesimal simplices</a>. I feel this improves considerably in its detail and exposition style over stuff I had previously typed at [[infinitesimal singular simplicial complex]] and eventually I will try to go through that entry and polish it accordingly. For the moment though I would just want to advertize: not that i think this is anything close to perfect, but in case anyone ever wondered where the heck actually the magic occurs in Anders Kock's discussion of combinatorial differential forms in a smooth topos: the crucial argument is a very elementary and simple one, which needs neither the (internal) topos (logic) perspective nor in fact the comparatively complicated (it seems) formulas from Breen-Messing's article, but is really just a simple statement about certain very simple finitely-presented commutative cosimplicial $\mathbb{R}$-algebras. This I try to expose at <a href="http://ncatlab.org/nlab/show/infinitesimal+object#SpacOfInfSimpl">Spaces of infinitesimal simplices</a>. I am not claiming that my exposition is not in need of more improvement, but it seems to me that this is a useful clarification (and if only a more focused highlighting) of some things one may find in some literature.

   I am now pretty much through with completing and polishing that section on Spaces of infinitesimal simplices.

   I feel this improves considerably in its detail and exposition style over stuff I had previously typed at infinitesimal singular simplicial complex and eventually I will try to go through that entry and polish it accordingly.

   For the moment though I would just want to advertize: not that i think this is anything close to perfect, but in case anyone ever wondered where the heck actually the magic occurs in Anders Kock’s discussion of combinatorial differential forms in a smooth topos: the crucial argument is a very elementary and simple one, which needs neither the (internal) topos (logic) perspective nor in fact the comparatively complicated (it seems) formulas from Breen-Messing’s article, but is really just a simple statement about certain very simple finitely-presented commutative cosimplicial $\mathbb{R}$-algebras. This I try to expose at Spaces of infinitesimal simplices. I am not claiming that my exposition is not in need of more improvement, but it seems to me that this is a useful clarification (and if only a more focused highlighting) of some things one may find in some literature.

5. • CommentRowNumber5.
   • CommentAuthornLab edit announcer
   • CommentTimeMar 5th 2023
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexIt was stated below definition 2.1 that an internally small object is an externally small object (the corresponding nLab page about tiny objects was linked). I believe that this is incorrect, so I edited the paragraph accordingly. Nico Beck <a href="https://ncatlab.org/nlab/revision/diff/infinitesimal+object/48">diff</a>, <a href="https://ncatlab.org/nlab/revision/infinitesimal+object/48">v48</a>, <a href="https://ncatlab.org/nlab/show/infinitesimal+object">current</a>

   It was stated below definition 2.1 that an internally small object is an externally small object (the corresponding nLab page about tiny objects was linked). I believe that this is incorrect, so I edited the paragraph accordingly.

   Nico Beck

   diff, v48, current