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14 / 7 / 11 / ?

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  No. 351
>>376 >>490 >>492 >>929
(please move to /adv/ if this belongs there)

I started with category theory a week ago with Lane's book. It's a bit hard and there are some examples (like lie groups) that I don't quite get. Related to this I've read Fraleigh's book on abstract algebra. Is this enough background or should I wait a bit before getting into category theory?

Thanks
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  No. 376
>>351

https://www.youtube.com/watch?v=yAi3XWCBkDo
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  No. 488 >>490

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Lie groups are more interesting than category theory anyway. You should switch to reading Cartan for Beginners.
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  No. 490
>>351
Bookrel is pretty good! It's definitely not a cakewalk though, you really have to pay attention and work through each example. Your post is a bit old now so I'm curious how your progress went.

>>488
>Cartan for beginners
That is pretty advanced for someone just now seeing categories.
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  No. 491 >>492 >>565
Can someon explain me:
What is Category-theory even about?
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  No. 492
>>491
>>351
See:
>https://arxiv.org/abs/1802.06221

I don't get it all. I understand what set theory and type-theory is about... but I don't get Categories... :-(
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  No. 565 >>567

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>>491
>Can someon explain me:
>What is Category-theory even about?
Category Theory is a substitute for set theory when you're someone who studies abstract algebra.
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  No. 567 >>568
>>565
Can you explain which is the demand for category theory? Or its just because sets arn't kate-gory enough?

Frankly, I don't get it.
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  No. 568 >>570 >>573

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>>567
Not >565 but category theory comes in handy to formulate many concepts, it's a useful language to have.

For example often one will have already established what a "morphism" is and would like to also have the notion of "isomorphism". Category theory tells one that the latter notion follows from the former while having all the desirable properties. Similiar applies to say the notion of product or coproduct.

This also allows one to develop machinery and tools in the abstarct context of category theory, e.g. homological algebra in Abelian categories, and then apply those tools in many different contexts, e.g. homological algebra for R-modules, or sheaves of R-modules, etc..
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  No. 570 >>571

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>>568
Would you say that if set theory is the skeleton, then category theory is the connecting tissue?
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  No. 571 >>573

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>>570
Due to the way things end up being I'd say it's not an unfair analogy to draw. However primarily I'd say they're a priori just two different languages for describing maths.
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  No. 573 >>575
>>568
>Not >565 but category theory comes in handy to formulate many concepts, it's a useful language to have.

And why is it better than set theory, HOL or mereology?
(Or even some kind of formal ontology in the informatics)

As far as I understand, you could easly define a predicate "x is isomorph to y" := Iso(y,x) and work with this.
Okay, I see the advantage of a graphical picture.

What I have see in categories looks suspicies like a usual powerset.

Or I'm just to simple-minded to get it at all?

>>571
Okay.

As far as I see, the central relation in set theory is the "being part of", maybe in the HOL is more "impled".
What is the categories about?
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  No. 575
>>573
First of all I wouldn't say it's "better" than set theory or higher order logic.
Second of all you can't just easily define a predicate "is isomorphic to", well you can, but it's useless and you're missing the point. You want to define it in a way for it to have the desirable properties and if you just define a predicate, then you have to figure out how to piece it into the rest of the theory.
Third of all higher order logic is fundamentally different from set theory or category theory, as it's part of the deductive system of your theory, not part of the actual things you talk about. So indeed I'd say yes you're being too simple minded/delusional to get it right now.

As to what category theory is "about" is I'd say morphisms, the same way set theory is abour membership, since morphisms are what ought to be defined to speak of a category and draw the beloved arrows.
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  No. 928

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So did you end up doing category theory?
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  No. 929
>>351
you lack basically all motivation. read bott tu and brown's topology first. and then vaisman's book on cohomology as an intro to cats

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