Timeline for Lawvere's "Some thoughts on the future of category theory."
Current License: CC BY-SA 3.0
14 events
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| Feb 11, 2013 at 14:28 | comment | added | Todd Trimble | I was just clarifying, since it might not have been obvious to a reader what the topos of super-sets is. ("Super-set" is usually contrasted with "subset", as a google search for super-set will indicate.) | |
| Feb 9, 2013 at 20:28 | comment | added | Urs Schreiber | In particular this sheaf-theoretic perspective on supergeometry does away with the problem of the approach of de Witt (possibly the most popular approach among practitioners!) which starts with "fix some infinite-dimensional Grassmann algebra, it won't matter which one, but fix one". Instead of this hack, the sheaf-theoretic formulation correctly formalizes what "it won't matter which one but fix one" really means: namely that all constructions are to be such that they can be evaluated on any Grassmann algebras and that they are covariant in the choices. Hence presheaves. | |
| Feb 9, 2013 at 20:25 | comment | added | Urs Schreiber | That's right. (Is your comment part of some discussion? I am asking because I don't see what you are replying to.) The topos over superpoints is discussed here: ncatlab.org/nlab/show/super+infinity-groupoid . The observation that super-mathematics (superalgebra and supermanifold theory) is really to be thought of as taking place over the base topos of sheaves on superpoints is due to Albert Schwarz, V. Molotkov, and Alexander Voronov, who all introduced this in 1984 (apparently idependently?!). I think this is abstractly the right way to go about supermathematics. | |
| Feb 9, 2013 at 19:27 | comment | added | Todd Trimble | If I'm not mistaken, by topos of "super-sets", Urs means the sheaf topos of super-points as explained here: ncatlab.org/nlab/show/superpoint | |
| Apr 30, 2011 at 10:56 | history | edited | Urs Schreiber | CC BY-SA 3.0 |
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| Apr 29, 2011 at 18:02 | vote | accept | David Spivak | ||
| Apr 29, 2011 at 10:58 | history | edited | Urs Schreiber | CC BY-SA 3.0 |
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| Apr 29, 2011 at 7:25 | history | edited | Urs Schreiber | CC BY-SA 3.0 |
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| Apr 29, 2011 at 5:19 | history | edited | Urs Schreiber | CC BY-SA 3.0 |
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| Apr 28, 2011 at 19:51 | history | edited | Urs Schreiber | CC BY-SA 3.0 |
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| Apr 28, 2011 at 18:36 | history | edited | Urs Schreiber | CC BY-SA 3.0 |
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| Apr 28, 2011 at 18:27 | history | edited | Urs Schreiber | CC BY-SA 3.0 |
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| Apr 28, 2011 at 16:48 | history | edited | Urs Schreiber | CC BY-SA 3.0 |
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| Apr 28, 2011 at 16:42 | history | answered | Urs Schreiber | CC BY-SA 3.0 |