Timeline for Examples of toposes for analysts
Current License: CC BY-SA 3.0
8 events
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| Dec 19, 2013 at 20:43 | comment | added | Anton Fetisov | @TomLaGatta, not exactly true. Synthetic diff. geom. is more about providing a model which allows one to work with infinitely small or infinitely large numbers. In this sense it is like a topos-theoretic version of nonstandard analysis, however it has categorical rather than logical flavor and allows a wider variety of models (e.g. existence of nilpotent infinitesimals and analogies with algebraic geometry). | |
| Dec 18, 2013 at 21:33 | comment | added | Steven Landsburg | @TomLaGatta: I'm not familiar with the literature on toposes and lexicographic preferences (and my initial uneducated reaction is to wonder how toposes could possibly be useful in this context), but you've inspired me to dig around a little. If I find something interesting, I'll report back. | |
| Dec 18, 2013 at 19:23 | comment | added | Tom LaGatta | @StevenLandsburg, thanks much for the useful pointer. On the nLab page, it says, "These models are constructed in terms of sheaf toposes on the category of smooth loci, formal duals to C∞-rings. See there for a detailed list of references." That's too abstract for me to understand. Is there an example topos which is relevant to economic or physical applications? A friend was telling me about "lexicographical preferences", which are supposedly well-modeled using synthetic differential geometry. Is there a topos of note in that setting? en.wikipedia.org/wiki/Lexicographic_preferences | |
| Dec 18, 2013 at 19:08 | comment | added | Steven Landsburg | @TomLaGatta: Fair enough. It wasn't clear from your question that you were already aware of this subject, so I thought it might point you in a helpful direction. | |
| Dec 18, 2013 at 19:00 | comment | added | Tom LaGatta | @StevenLandburg, synthetic differential geometry is interesting, but I don't see how this answers my question regarding specific toposes of interest to analysts. The entire approach of synthetic differential geometry seems to begin synthetically rather than analytically: with a topos $E$ in hand, differental geometric structures are built. My question is in the opposite direction: what are some such toposes $E$ which might be of interest to analysts? ncatlab.org/nlab/show/synthetic+differential+geometry | |
| Dec 18, 2013 at 17:47 | review | Low quality posts | |||
| Dec 18, 2013 at 17:58 | |||||
| S Dec 18, 2013 at 17:32 | history | answered | Steven Landsburg | CC BY-SA 3.0 | |
| S Dec 18, 2013 at 17:32 | history | made wiki | Post Made Community Wiki by Steven Landsburg |