gfixler 2017-02-06 16:58:35
I come bearing CT questions
gfixler 2017-02-06 16:58:54
objects can have multiple arrows between them?
gfixler 2017-02-06 16:59:09
i.e. A -f-> B, A -g-> B, etc.
erisco 2017-02-06 16:59:26
yes
erisco 2017-02-06 16:59:32
but don't make the questions too much harder for me :P
gfixler 2017-02-06 16:59:37
hehe
gfixler 2017-02-06 16:59:56
I'm wondering if Hask can have multiple such arrows
gfixler 2017-02-06 17:00:23
I have learned that a category of relations can't have multiple arrows of the same direction between any 2 objects
gfixler 2017-02-06 17:00:38
though you could have A -> B and B -> A
gfixler 2017-02-06 17:01:19
I'm not sure what that means, though
gfixler 2017-02-06 17:01:34
I would presume A >= B the other way becomes B <= A
Koterpillar 2017-02-06 17:02:22
gfixler: if A and B are types, of course there can be multiple functions of type A -> B
gfixler 2017-02-06 17:02:44
Koterpillar: okay, so the morphisms are functions
gfixler 2017-02-06 17:02:55
I seem to always mix up which level of reasoning I'm in with CT
gfixler 2017-02-06 17:03:21
Koterpillar: another question: Not every object pair must have an arrow, right?
Koterpillar 2017-02-06 17:03:24
I'm going by https://wiki.haskell.org/Hask
erisco 2017-02-06 17:03:29
correct
Koterpillar 2017-02-06 17:03:29
gfixler: correct
gfixler 2017-02-06 17:03:39
good, this is clicking
erisco 2017-02-06 17:03:58
you're just obligated to have composition and identity
gfixler 2017-02-06 17:04:08
right
erisco 2017-02-06 17:04:51
then often additional properties are added, but that is the minimum
gfixler 2017-02-06 17:05:19
the property of totally rocking
erisco 2017-02-06 17:05:36
you could add that if f : A -> B and g : A -> B then f = g
gfixler 2017-02-06 17:06:05
that's not just a given?
gfixler 2017-02-06 17:06:20
so in Hask, I suppose it wouldn't be
erisco 2017-02-06 17:06:41
no it isn't a given
gfixler 2017-02-06 17:06:41
f could be `length` and g could be `number of vowels`
erisco 2017-02-06 17:06:55
so you can say you want to talk about categories with that property and then derive theorems
gfixler 2017-02-06 17:07:03
cool
erisco 2017-02-06 17:07:04
then you can later prove that particular instances have that property
erisco 2017-02-06 17:07:11
then you know the theorems must also hold
gfixler 2017-02-06 17:07:13
just that alone makes my mind explode
gfixler 2017-02-06 17:07:22
a whole text book appeared in my head of new things
erisco 2017-02-06 17:07:45
well that is just mathematics generally, not only CT
gfixler 2017-02-06 17:07:49
right
gfixler 2017-02-06 17:08:00
I'm new to these more interesting maths
erisco 2017-02-06 17:08:07
same if you start with a magma and add an identity
gfixler 2017-02-06 17:08:08
so I keep finding such properties impressive
gfixler 2017-02-06 17:08:11
yep
gfixler 2017-02-06 17:08:55
hey, that property you just mentioned seems to define thin categories
gfixler 2017-02-06 17:09:03
https://ncatlab.org/nlab/show/thin+category
gfixler 2017-02-06 17:09:11
I had just opened that on the other screen a moment ago
erisco 2017-02-06 17:09:21
seems so, I didn't know that :)
wolphin 2017-02-06 17:38:39
I have GUI that is just nice interface for a config file. When user changes something I can just print what have been changed to stdout (using signals from GUI), then parse that data with second program and make changes to the config. Looks like I need something similar to global state to do that job inside one program?
