Timeline for Why the term "monad" in homological algebra?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 31, 2014 at 23:12 | vote | accept | Qfwfq | ||
| Jan 24, 2014 at 3:04 | comment | added | Peter May | Todd, apologies to me? For what? As correctly reported in the link you give, I persuaded MacLane to use the (preexisting) term monad in place of triple in his book. No claim that either Saunders or I introduced the term (I'm guilty of the name ``operad'', part of the point of which is that it goes so nicely with monad.) | |
| Jan 23, 2014 at 20:12 | comment | added | Peter LeFanu Lumsdaine | @ToddTrimble: I’d vote against making this CW. The answers so far are indeed speculative (though not equally so); but it’s easy to imagine a better answer coming along that was less speculative. (For instance, a reference to a paper from around when the term was introduced, giving an explanation or motivation for the term; or even a personal recollection like Sasha’s in comments, but with clearer attribution.) | |
| Jan 23, 2014 at 17:24 | comment | added | Todd Trimble | I'm thinking about making this CW, since the answers so far look like guesswork to me. What do people think? | |
| Jan 23, 2014 at 17:16 | answer | added | user42369 | timeline score: 5 | |
| Jan 22, 2014 at 9:05 | answer | added | Carlo Beenakker | timeline score: 4 | |
| Jan 22, 2014 at 9:05 | comment | added | Sasha | The term monad in the sense of Wikipedia article you are referring to of course sounds strange. A triad could be more appropriate. But I heard that it sounded a bit obscene at that time, so people used monad instead. | |
| Jan 22, 2014 at 5:23 | comment | added | Manfred Weis | To my knowledge, the term monad has been 'invented' by Leibniz; maybe knowing his understanding of the term gives some clues, why it is used in certain mathematical contexts. | |
| Jan 22, 2014 at 0:50 | comment | added | Todd Trimble | Well, I learned something new. There seems to be a reasonable consensus that the term "monad" in category theory is due to Benabou (with apologies to Peter May): english.stackexchange.com/a/30661. | |
| Jan 22, 2014 at 0:02 | comment | added | Peter LeFanu Lumsdaine | One other mathematical usage of monad comes to mind: in logic, unary predicates (i.e. “X is a dog”, but not relations like “X loves Y”) are called monadic predicates, and predicate logic based just on monadic predicates is called monadic logic. The earliest use of this terminology I can find is 1956, when Halmos wrote a paper titled monadic Boolean algebras, but the study of such logics goes back a couple of decades further, and I suspect the terminology does as well, though my google-fu is failing me. | |
| Jan 21, 2014 at 23:24 | comment | added | Tom Leinster | I don't know why they're called that, but the Wikipedia article you link to dates this usage to 1964, whereas I'm pretty sure the category theory usage was coined later than that (late 1960s, I guess). You weren't asking this, but I might as well add: in category theory, the word "monad" is intentionally like "monoid", since from an appropriately elevated viewpoint, monads and monoids are the same thing. | |
| Jan 21, 2014 at 22:54 | history | asked | Qfwfq | CC BY-SA 3.0 |