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https://arxiv.org/abs/1612.09375

It starts with the basics and it leads up to a trio of related concepts, which are all ways of talking about universal properties.

Huh? What's a 'universal property'?

In category theory, we try to describe things by saying what they

A

Universal properties show up in three closely connected ways in category theory, and Tom's book explains these in detail:

through

through

through

If you want to see this vague wordy mush here transformed into precise, crystalline beauty, read Tom's book! It's not easy to learn this stuff - but it's good for your brain. It literally rewires your neurons.

Here's what he wrote, over on the category theory mailing list:

.............................................................................

Dear all,

My introductory textbook "Basic Category Theory" was published by Cambridge University Press in 2014. By arrangement with them, it's now also free online:

https://arxiv.org/abs/1612.09375

It's also freely

There are lots of good introductions to category theory out there. The particular features of this one are:

• It's short.

• It doesn't assume much.

• It sticks to the basics.

**Tom Leinster**has written a great introduction to that wonderful branch of math called category theory! It's free:https://arxiv.org/abs/1612.09375

It starts with the basics and it leads up to a trio of related concepts, which are all ways of talking about universal properties.

Huh? What's a 'universal property'?

In category theory, we try to describe things by saying what they

*do*, not what they're*made of*. The reason is that you can often make things out of different ingredients that still*do*the same thing! And then, even though they will not be strictly the same, they will be**isomorphic**:*the same in what they do*.A

**universal property**amounts to a precise description of what an object*does*.Universal properties show up in three closely connected ways in category theory, and Tom's book explains these in detail:

through

**representable functors**(which are how you actually hand someone a universal property),through

**limits**(which are ways of building a new object out of a bunch of old ones),through

**adjoint functors**(which give ways to 'freely' build an object in one category starting from an object in another).If you want to see this vague wordy mush here transformed into precise, crystalline beauty, read Tom's book! It's not easy to learn this stuff - but it's good for your brain. It literally rewires your neurons.

Here's what he wrote, over on the category theory mailing list:

.............................................................................

Dear all,

My introductory textbook "Basic Category Theory" was published by Cambridge University Press in 2014. By arrangement with them, it's now also free online:

https://arxiv.org/abs/1612.09375

It's also freely

**editable**, under a Creative Commons licence. For instance, if you want to teach a class from it but some of the examples aren't suitable, you can delete them or add your own. Or if you don't like the notation (and when have two category theorists ever agreed on that?), you can easily change the Latex macros. Just go the arXiv, download, and edit to your heart's content.There are lots of good introductions to category theory out there. The particular features of this one are:

• It's short.

• It doesn't assume much.

• It sticks to the basics.

View 15 previous comments

- +David Jao I agree with your more refined use of the word 'free', but Tom could I presume only use the license that his publishing agreement lets him, since after all a publisher is actually selling copies.41w
- +David Jao - I wanted to tell everyone that they could get Tom's book without paying for it, and I said this in the fastest possible way, to make sure this fact appeared in the top two lines of the post - the part everyone sees.41w
- " the part everyone sees."

how practical

your outlook...our quick scrolling

ways...to get to the next post,

in that hurry the last lines

become the orphans...

I hope this is not too

'unpredictable...' the comment

sometimes it is way too hard

not to comment, even though I tell myself

I must not....

+John Baez always your good

intentions are appreciated.41w - +Shantha Hulme - we live in fast times, as if we're eager for the future and think it'll come faster if we all hurry - or afraid of the present and anxious to get it over with! I'm trying to slow down a bit, myself. A bit of unpredictable poetic 'sand in the machinery' helps.41w
- OK, tried to convert it to mobi, didn't make it. After spending an hour fiddling with the source and trying to make it compatible with htlatex, I gave up. PDF will have to be enough. :)41w
- A noble effort!41w

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