Timeline for Is there a name for relations with this property, and the category of them?
Current License: CC BY-SA 3.0
11 events
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| Oct 4, 2022 at 16:00 | comment | added | Tom Ellis | The earliest reference I know of to such relations related to parametricity is "Internalizing Relational Parametricity in the Extensional Calculus of Constructions" by Krishnaswami and Dreyer (2013). | |
| Jul 3, 2021 at 7:53 | comment | added | Tom Ellis | Robert Harper, in "Reynolds’s Parametricity Theorem, Directly" calls these "zig-zag complete" binary relations (cs.cmu.edu/~rwh/courses/chtt/pdfs/reynolds.pdf). | |
| Apr 17, 2020 at 12:40 | answer | added | arsmath | timeline score: 2 | |
| Sep 19, 2018 at 14:35 | comment | added | Arnaud D. | I've just posted an answer to the MSE question, but note that such relations are also called difunctional relations. In the category of sets, or any pretopos, they coincide with pullbacks, see for example tac.mta.ca/tac/volumes/27/1/27-01abs.html | |
| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
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| Oct 30, 2013 at 14:49 | answer | added | David Wilding | timeline score: 3 | |
| Oct 30, 2013 at 10:06 | answer | added | Boris Novikov | timeline score: 5 | |
| Oct 27, 2013 at 15:28 | comment | added | Tom Ellis | Interesting, Todd. Indeed operator theory might be a good place to look for an analogy. Perhaps the correct condition there would be $\rho = \rho\rho^*\rho$, where $\rho^*$ is the adjoint of $\rho$. This class would contain the orthogonal operators, for example. | |
| Oct 27, 2013 at 14:43 | comment | added | Todd Trimble | Whatever they might be called, this looks like an interesting notion. Remark that functions and opposites of functions form such relations. Also remark that the condition is equivalent to saying $\rho = \rho \rho^{op} \rho$ (literally the condition is saying "$\geq$", but "$\leq$" happens to be true for any relation $\rho$). I can't locate my copy of Categories, Allegories to see if Freyd-Scedrov introduce this notion, but I am vaguely reminded of von Neumann regular elements. | |
| Oct 27, 2013 at 10:04 | history | edited | Tom Ellis | CC BY-SA 3.0 |
add ct.category-theory
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| Oct 27, 2013 at 9:45 | history | asked | Tom Ellis | CC BY-SA 3.0 |