Timeline for What is the mathematical name for Haskell's Alternative Functor
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 11, 2017 at 9:11 | comment | added | მამუკა ჯიბლაძე | Sorry that was actually (next to) trivial - with the only sense for naturality of $e$ and $m$ that I can think of, it is immediate. | |
| Jan 10, 2017 at 14:06 | comment | added | Andrej Bauer |
@მამუკაჯიბლაძე: that's a good question. Staring at the official definition there does not seem to be that requirement. On the other hand they also have the some and many things which do have some connection to the Applicative class. Those might actually be more interesting than the monoid structure.
|
|
| Jan 9, 2017 at 21:37 | comment | added | მამუკა ჯიბლაძე | But do values of $F$ on morphisms come out monoid homomorphisms? I don't see it from what is given. | |
| Jan 9, 2017 at 14:04 | comment | added | Todd Trimble | Cartesian monoid object? Can't think of a better term for it at the moment. (Unfortunately you can't just call it a monoid object since there is also endofunctor composition as monoidal product. Remark that endofunctor composition $- \circ F$ preserves cartesian products, but obviously not so for $F \circ -$. There is some sort of weak/lax distribution for $F \circ -$ though if we add in Applicative.) | |
| Jan 9, 2017 at 13:47 | history | edited | Andrej Bauer | CC BY-SA 3.0 |
deleted 24 characters in body
|
| Jan 9, 2017 at 13:46 | comment | added | xuh | Thanks for the clarification. I'm not a mathematician. So it is much appreciated. I have one question: shouldn't the type of $e_A$ be $1 \rightarrow F(A)$? | |
| Jan 9, 2017 at 13:45 | comment | added | Dylan Wilson | Haven't you just described a factorization of the functor through the category of monoids in C? So an alternative functor is just a functor F: C---> Mon(C)? I guess we have to encode the lax-monoidal part... | |
| Jan 9, 2017 at 13:35 | history | answered | Andrej Bauer | CC BY-SA 3.0 |