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/sci/ - Science & Math

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5755920 No.5755920 [Reply] [Original]

Today I have to study the Eilenberg-Moore and Kleisli categories

Any tips? I get the idea of them roughly but I'm not sure I can remember it all

Anyone else working on revision? What are you all studying?

>> No.5755926 [DELETED] 

What textbook are you working out of? Mac Lane?

>> No.5755929

>>5755926
my own lecture notes. I have that book (categories for the working mathematician) and it's very nice.

>> No.5756021
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5756021

bump

>> No.5756033

>>5755920
Why are monads interesting?
The only thing I got out of the definition is a set-based construction of free algebraic things.

>> No.5756039

>>5756033
i don't even know which is pathetic and I'm ashamed of that but my course has thrown so so so much material at me in such a short time I have no chance to read more deeply about things like I usually would. I think they can be used to work abstractly with models of algebraic theories. The only use I've had for them in practice is programming languages semantics. There's also Beck's monadicity theorem which surely has some value I don't understand.

>> No.5756048 [DELETED] 
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5756048

>>5756033
http://golem.ph.utexas.edu/category/2007/05/cohomology_and_computation_wee_4.html

>> No.5756052

>>5756039
>my course has thrown so so so much material at me in such a short time I have no chance to read more deeply about things like I usually would
I know that feel, man.

I will probably have to learn this stuff too when when get into topos theory later on.

>> No.5756057
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5756057

> intending to study topos theory
PREPARE YOUR BRANUS

>> No.5756062

>>5756048
Granted the bar construction provides a conventient tool for constructing simplicial modules and whatnot, and I can see the application to Hochshild homology.
Still this seems like a very specialized application, and I doubt it alone warrants the "theory of monads".

>> No.5756084

I'm studying high school math.

Does anyone happen to know any good sites to practice? Preferably good lessons + practice.

>> No.5756089

>>5756084
this site is for 18+

>> No.5756091

>>5756084
p.s. people are going to tell you 'khan academy' if you ask that.. ignore them

>> No.5756093

>>5756084
Read a book. Serge Lang has a good book "Basic mathematics".

>> No.5756101
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5756101

>>5756057
How hard can it be~

>> No.5756115

>>5756089
You can be 18+ and be in high school. You can get a GED at 18+.

>> No.5756124

>>5756091
>people are going to tell you 'khan academy' if you ask that.. ignore them
>ignore them
Fool, are you serious? Khanacademy.org is a great site for learning high school math.

>> No.5756149

>>5756089
>>5756084
>>5756124
>>5756091
>>5756115
nice thread derail now can get back to the topic?

>> No.5756212

>>5756149
>math study thread
>"I'm ***studying*** high school ***math***"
>thread derail

>> No.5756218

>>5756212
> high school
> math
pick one

>> No.5756245

>>5756218
>you
>not gay

>> No.5756263

>>5756033
Monads are used extensively in Haskell to model sequential computation.

>>5755920
Kleisli categories are also applied in Haskell as a certain type of arrow. Arrows are a more powerful way of modeling computation in Haskell.

If you understand category theory, Haskell is easier to learn.

>> No.5756268
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5756268

>>5756263
>programming
>computer science

>> No.5756390

I haven't been able to get myself to study all day.. feel like shit