Timeline for On the History of Double Adjoints
Current License: CC BY-SA 3.0
18 events
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| Dec 4, 2017 at 14:58 | comment | added | Javier Arias | Thanks a lot for the info. I still would love to know if double adjoints were already discovered in the 60s )when Zellig Harris started to study mathematical structures in language) or whether they were developed later, so that only in the 90s or so could Lambek incorporate them into the formal study of natural language. Any feedback on the chronology would be immensely appreciated. | |
| Dec 4, 2017 at 12:49 | comment | added | peter a g | (cont) This has a right adjoint, the inverse image $f^*\colon P(Y) \to P(X)$ and $f^*$ has a right adjoint $f_!\colon P(X) \to P(Y)$, called the universal image and defined for a subset $A$ of $X$ by $f_!(A)$ consists of the elements of $Y$ all of whose inverse images lie in $A$. | |
| Dec 4, 2017 at 12:49 | comment | added | peter a g | Personal communication from Michael Barr: there is really no theory or history of double adjoints. Just that in some cases, a right (say) adjoint to a functor has a further right adjoint. The most obvious example of this is that a function $f\colon X \to Y$ induces the function direct image on the power sets (partially ordered sets considered as categories) $f_*\colon P(X) \to P(Y)$. (cont) | |
| Dec 3, 2017 at 17:21 | comment | added | Javier Arias | math.mcgill.ca/rags/JAC/124/Lambek-Pregroups-s.pdf | |
| Dec 3, 2017 at 3:41 | comment | added | Mike Shulman | The link is 15 pages long, and searching for the word "double" turns up only one occurrence on page 7, which is not a definition. | |
| Dec 2, 2017 at 7:12 | review | Close votes | |||
| Dec 7, 2017 at 19:58 | |||||
| Dec 2, 2017 at 3:48 | comment | added | Javier Arias | Well, the link I provided gives that info. That is one of the sources of my reading....I hope it helps | |
| Dec 1, 2017 at 21:16 | comment | added | Mike Shulman | If you want people to answer your question, it's kind to them to include definitions of your terminology in the question, especially if it's nonstandard. | |
| Dec 1, 2017 at 19:44 | comment | added | Javier Arias | If you read this you will grasp it: math.mcgill.ca/barr/lambek/pdffiles/logicandgr.pdf | |
| Dec 1, 2017 at 19:02 | comment | added | Mike Shulman | What is a "double adjoint"? | |
| Dec 1, 2017 at 6:46 | history | edited | Ben McKay | CC BY-SA 3.0 |
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| Dec 1, 2017 at 6:21 | history | edited | YCor |
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| Dec 1, 2017 at 6:21 | comment | added | YCor | crossposted after one hour | |
| Nov 30, 2017 at 15:46 | history | edited | Javier Arias | CC BY-SA 3.0 |
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| Nov 30, 2017 at 15:42 | comment | added | Noah Schweber | Crossposted from math.stackexchange.com/questions/2544546/…. | |
| Nov 30, 2017 at 15:33 | history | edited | Javier Arias | CC BY-SA 3.0 |
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| Nov 30, 2017 at 15:30 | review | First posts | |||
| Nov 30, 2017 at 15:51 | |||||
| Nov 30, 2017 at 15:26 | history | asked | Javier Arias | CC BY-SA 3.0 |