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added a section Spaces of infinitesimal simplices
FYI: If you have a typo in the subject of a post, you can change it by editing the original comment.
Thanks, Eric! I didn’t know that, but did wonder about it. Good, so I fixed the typo.
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.
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