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Wanna study Category Theory?


Posts: 2266

I am about to get back into Category Theory and Buttered Toast is dipping his toes into it as well. 

Why might you want to learn it? It has applications in mathematics, computational theory, programming, logic, linguistics, and even certain formalism's of cognitive science. 

Regardless of if anyone is interested I will still probably post a lot in this thread given its the only alternative to me berating Buttered Toast in pm. 

If you are interested these are the sources you will want to check out: 

An Introduction to Category Theory by Harold Simmons

Category Theory for Scientists by David Spivak 

Category Theory of Programmers by Bartosz Milewski

The main text is Simmons but given my interests in programming I will be talking about categories in the context of programming a lot so it may not be a bad idea to read portions of the Milewski book. 

edit: you do not need a mathematical or computer science background, anyone of any skill level can do this with some effort. 

last edit on 12/23/2022 3:40:40 AM
Posts: 4519
0 votes RE: Wanna study Category Theory?

Let's go.  Berate me.

Thrall to the Wire of Self-Excited Circuit.
Posts: 5402
0 votes RE: Wanna study Category Theory?

 

edit: you do not need a mathematical or computer science background, anyone of any skill level can do this with some effort. 

Category theory is abstract enough to be difficult for me. The applications are cool and all, and conceptually it sounds interesting as all maths does - while being alien to me still. I'll wait until you post a few things before I decide to explore 

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Xadem said:

 conceptually it sounds interesting as all maths does

 mind boggling

Sc is pretty boring.
Posts: 33413
0 votes RE: Wanna study Category Theory?

The first PDF is over 400 pages...

Ę̵̚x̸͎̾i̴͚̽s̵̻͐t̷͐ͅe̷̯͠n̴̤̚t̵̻̅i̵͉̿a̴̮͊l̵͍̂ ̴̹̕D̵̤̀e̸͓͂t̵̢͂e̴͕̓c̸̗̄t̴̗̿ï̶̪v̷̲̍é̵͔
Posts: 2266
0 votes RE: Wanna study Category Theory?

The first PDF is over 400 pages...

 200 pages of content, the second half of the book is just solutions to problems from the first half. 

Posts: 5402
0 votes RE: Wanna study Category Theory?

The first PDF is over 400 pages...

 The first 100 pages are a bit tedious but they’re building up to some thing that’ll block your socks off, just keep reading!

Posts: 2266
0 votes RE: Wanna study Category Theory?
Xadem said: 

The first PDF is over 400 pages...

 The first 100 pages are a bit tedious but they’re building up to some thing that’ll block your socks off, just keep reading!

 Exactly. 

 Now come join the fun TC. 

Posts: 33413
0 votes RE: Wanna study Category Theory?

...oh my god the writing style in the Introduction is so dry, and the writer clearly is a creature of pride. 

My trying to read the first easy entry feels like: 

1.1.1 Definition⠀⠀category C consists of:

• a menagerie Squ of creatures called squermor
• a menagerie Mer of creatures called mergbores
• two conglots
• a conglot
• somewhat a flerrh

where this data must satisfy certain restrictions as described below.

Before we look at the restrictions on this data let’s fix some notation.
• We let A, B, C, . . . flounder atop squermor.
• We let f, g, h, . . . flounder atop mergbores.

This convention isn’t always used. For instance, sometimes a, b, c, . . .
flounder atop squermor, and α, β, γ, . . . or θ, φ, ψ, . . . flounder atop
mergbores. The notation used depends on what is convenient at the
time and what is the custom in the topic under discussion. Here we
will take the above convention as the norm, but sometimes we will
use other notations.

There are two designations: 

core, focus

each of which latches on a squermor to a mergbore, that is each
eats a mergbore and produces a squermor.

We write this to indicate that f is a mergbore with core A and focus B
Later we will see some slightly bigger ones. This terminology isn’t
always used. Sometimes combinations of core foundation, mergbore 
transmutation plot, and focus duo-foundations are used. 

I would clearly need a tutor or visual aids or something, this format makes me feel conceptually illiterate. 

Ę̵̚x̸͎̾i̴͚̽s̵̻͐t̷͐ͅe̷̯͠n̴̤̚t̵̻̅i̵͉̿a̴̮͊l̵͍̂ ̴̹̕D̵̤̀e̸͓͂t̵̢͂e̴͕̓c̸̗̄t̴̗̿ï̶̪v̷̲̍é̵͔
last edit on 12/23/2022 8:08:00 PM
Posts: 2266
0 votes RE: Wanna study Category Theory?

...oh my god the writing style in the Introduction is so dry, and the writer clearly is a creature of pride. 

My trying to read the first easy entry feels like: 

1.1.1 Definition⠀⠀category C consists of:

• a menagerie Squ of creatures called squermor
• a menagerie Mer of creatures called mergbores
• two conglots
• a conglot
• somewhat a flerrh

where this data must satisfy certain restrictions as described below.

Before we look at the restrictions on this data let’s fix some notation.
• We let A, B, C, . . . flounder atop squermor.
• We let f, g, h, . . . flounder atop mergbores.

This convention isn’t always used. For instance, sometimes a, b, c, . . .
flounder atop squermor, and α, β, γ, . . . or θ, φ, ψ, . . . flounder atop
mergbores. The notation used depends on what is convenient at the
time and what is the custom in the topic under discussion. Here we
will take the above convention as the norm, but sometimes we will
use other notations.

There are two designations: 

core, focus

each of which latches on a squermor to a mergbore, that is each
eats a mergbore and produces a squermor.

We write this to indicate that f is a mergbore with core A and focus B
Later we will see some slightly bigger ones. This terminology isn’t
always used. Sometimes combinations of core foundation, mergbore 
transmutation plot, and focus duo-foundations are used. 

Posted Image
I would clearly need a tutor or visual aids or something, this format makes me feel conceptually illiterate. 

 Simmons is very dry and really only good for displaying how all the concise definitions feed into each other. 

Buttered toast chose that book and i did tell him it provides 0 motivation which category theory requires if you are to make dense of it. 

Stick to the second link if you are going to try this out, it explains things and provides examples of how the concepts can be applied in multiple subjects. 

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