dolio 2017-02-03 09:45:50
bicategory is a sort of 2-category.
dolio 2017-02-03 09:46:28
0-cells are categories, 1-cells are profunctors between categories, 2-cells are natural transformations.
dolio 2017-02-03 09:49:09
If you take the 1 and 2 levels of a bicategory above a single 0-cell (so, the endo-1-cells), you get a monoidal category. And the monads in the bicategory are monoids in the monoidal catgory.
dolio 2017-02-03 09:50:00
I should say, my description was of what the Prof bicategory is.
dolio 2017-02-03 09:50:39
A bicategory in general has 0-cells, 1-cells between pairs of 0-cells, and 2-cells between pairs of compatible 1-cells.
dolio 2017-02-03 09:51:00
And identities and composition and whatnot.
mniip 2017-02-03 09:53:50
I don't think I have that strong of a grasp on higher CT
dolio 2017-02-03 09:54:08
You can also make any monoidal category into a 1-object bicategory, and then the monoids in that monoidal category are monads in that bicategory.
dolio 2017-02-03 09:54:55
Kind of similar how you can make a monoid into a 1-object category.
dolio 2017-02-03 09:58:05
mniip: The 'obvious' example is category theory and monads.
dolio 2017-02-03 09:58:29
There's a bicategory with categories as the 0-cells, functors as the 1-cells and natural transformations as the 2-cells.
dolio 2017-02-03 09:59:01
And monads in that bicategory are the usual definition of monads.
dolio 2017-02-03 09:59:47
And when people talk about monads being monoids, that's taking one category (0-cell) and considering the monoidal category of endofunctors (endo-1-cells) and transformations.
mniip 2017-02-03 10:00:54
right
dolio 2017-02-03 10:00:55
Bicategories and monads in a bicategory let you talk about them within one whole structure instead of a bunch of similar ones.
mniip 2017-02-03 10:05:03
I have no idea what any of that means :p
monochrom 2017-02-03 10:17:51
erisco: In 1985, Wadler actually made the paper "how to replace failure by a list of successes", and it actually got accepted to a conference. So apparently the idea was considered impressive in the early days.
monochrom 2017-02-03 10:19:12
Although, the subtitle "a method for exception handling, backtracking, and pattern matching in lazy functional languages" was more impressive.
monochrom 2017-02-03 10:20:04
Sometimes you've got to measure an idea not by how easy to explain the solution, but how long it took the research community to think it up.
monochrom 2017-02-03 10:21:12
It was impressive to say "I have a way to unify exception and backtracking". (I think it still is.) You just feel anti-climatic because the punchline is "use [a]".
bbear 2017-02-03 10:23:26
what language should I learn next ?
bbear 2017-02-03 10:23:28
now ?
bbear 2017-02-03 10:23:31
Why ?
bbear 2017-02-03 10:23:33
Java ?
monochrom 2017-02-03 10:23:43
Today I would explain the idea level-headed and wouldn't make a big fuss about it, to be sure. It's 2017 already, we don't get easily excited by while-loops and the [] monad.
bbear 2017-02-03 10:23:53
[]
bbear 2017-02-03 10:23:56
[]
bbear 2017-02-03 10:23:58
[]
bbear 2017-02-03 10:24:03
\o/ monochrom
bbear 2017-02-03 10:25:29
was wondering if digging into real project is better for learning the language
bbear 2017-02-03 10:25:37
than doing noob tutorials.
bbear 2017-02-03 10:25:43
noob is not pejorative here
mniip 2017-02-03 10:26:04
huh
mniip 2017-02-03 10:26:22
if F is a functor C^op x C -> D, what does F(C, f) denote?
bbear 2017-02-03 10:26:26
looking into that https://wiki.haskell.org/Web/Frameworks that's plenty of meat
mniip 2017-02-03 10:26:48
F(id_C, f) ?
bbear 2017-02-03 10:28:24
monochrom: do you have a job ?
monochrom 2017-02-03 10:29:48
Not at the moment.
bbear 2017-02-03 10:31:01
what are you doing ?
monochrom 2017-02-03 10:31:16
Learning linear algebra.
bbear 2017-02-03 10:31:24
how old are you ?
monochrom 2017-02-03 10:31:31
No comment.
Tuplanolla 2017-02-03 10:31:57
Old enough to learn linear algebra, I hope.
bbear 2017-02-03 10:32:01
are you working with infinite dimensions or not yet ?
mniip 2017-02-03 10:32:02
what kind of linear algebra :o
monochrom 2017-02-03 10:32:12
Still finite dimension.
monochrom 2017-02-03 10:33:05
Finite dimension, complex scalars, the standard inner product, unit vectors under the 2-norm, unitary matrices and self-adjoint matrices.
bbear 2017-02-03 10:33:08
but why are you learning linear algebra ? Is it R-algebra or C-algebbra ?
mniip 2017-02-03 10:33:27
monochrom, that sounds simple enough
bbear 2017-02-03 10:33:29
monochrom: that's trivial matter for undergrad students in most countries
bbear 2017-02-03 10:33:35
well not so trivial
bbear 2017-02-03 10:33:50
but still that's the ground on which you build mathematics
monochrom 2017-02-03 10:33:55
If you think that my secret agenda is quantum something, you're right.
bbear 2017-02-03 10:33:57
at a higher level.
mniip 2017-02-03 10:34:19
monochrom, somehow you gave an impression of already knowing that :o
bbear 2017-02-03 10:35:20
well being able to define mathematically a monad gives you extra buckets that will pay your ticket outside of undergrad zone I would have bet but may be i am mistaked.
bbear 2017-02-03 10:35:38
and quantum mechanics is cool as well.
mniip 2017-02-03 10:35:43
bbear, can you define a monad?
bbear 2017-02-03 10:35:46
nope
Tuplanolla 2017-02-03 10:35:48
Where are we going with this, bbear?
bbear 2017-02-03 10:35:55
Nowhere
bbear 2017-02-03 10:35:59
absolutely nowhere
mniip 2017-02-03 10:36:05
idunno, I know 3 definitions and they are yet to come up useful :P
bbear 2017-02-03 10:36:28
3 definitions
monochrom 2017-02-03 10:36:34
I can define 5 monads.
mniip 2017-02-03 10:37:18
no like, define what a monad is in 3 separate ways
mniip 2017-02-03 10:37:57
maybe 6
mniip 2017-02-03 10:38:12
er, I meant maybe 4
bbear 2017-02-03 10:38:16
!monad
mniip 2017-02-03 10:38:19
your 5 distracted me
bbear 2017-02-03 10:38:30
mniip: anyway. Linear algebra is kewl
mniip 2017-02-03 10:38:35
sure is
dmwit 2017-02-03 10:39:04
mniip: I think F(C, f) denotes (f.)
monochrom 2017-02-03 10:39:07
I can do 2 off the top of my head. The usual 2 anyway. I can do 2 more if you let me re-watch some catster lectures first. (The Kleisli story and the Eisensomething story?)
mniip 2017-02-03 10:39:13
dmwit, and that is?
dmwit 2017-02-03 10:39:35
like, \g -> f . g
mniip 2017-02-03 10:39:50
monochrom, NTs, monoids, kleislis, and then specifically monoids in Hask as polymorphic data structures
dmwit 2017-02-03 10:40:25
mniip: Never mind. I'm confused and thinking of the Hom functor, which F is not necessarily. Sorry.
bbear 2017-02-03 10:41:05
scala is ok for FP ?
byorgey 2017-02-03 10:41:06
monochrom: Eilenberg-Moore?
monochrom 2017-02-03 10:41:14
yeah that one
byorgey 2017-02-03 10:41:34
yeah, I'd have to rewatch the catster lectures too =)
byorgey 2017-02-03 10:41:44
I'm just good at remembering names.
mniip 2017-02-03 10:42:01
I'm yet to learn what that is :p
dmwit 2017-02-03 10:42:06
mniip: Yes, I think F(id_C, f)
dolio 2017-02-03 10:42:24
dmwit: Which specializes to what you thought for the case of hom.
mniip 2017-02-03 10:42:30
dmwit, yeah that'd make sense
merijn 2017-02-03 10:43:00
nitrix: Can you explain what you meant with you 'Link' type you mentioned earlier today?
knupfer 2017-02-03 10:43:27
These join points are so intriguing!
dmwit 2017-02-03 10:43:48
mniip: As I recall from the one or two pages of MacLane that I managed to read, some people don't even both defining objects in the first place, using the id arrows as the objects.
dmwit 2017-02-03 10:44:07
mniip: Perhaps whatever source you're perusing is making that identification.
