Comment author:VKS
08 April 2012 12:08:05PM
*
4 points
[-]

Hello!

I should have read this post before I started posting.

I'm here because figuring out how thinking works is something I am interested in doing. I'm a freshman student in mathematics somewhere on planet Earth, but I know an unpredictable amount of mathematics beyond what I am supposed to. Particularly category theory. <3 Cat. Terrible at it for now though.

I hope I can say things which are mostly interesting and mostly not wrong, but my posting record already contains a certain number of errors in reasoning...

Comment author:VKS
27 April 2012 12:07:47AM
3 points
[-]

As dlthomas says, Cat is the category of all (small) categories. (The small is there in certain (common (?)) axiomatizations only, in which CAT is the quasi-category of all categories.) In abjectly terrible metaphor, a category can be taken as a mathematical structure which represents a particular field of mathematics. So you have things like Grp, the category of groups and group homomorphisms, for group theory, Top, which contains topological spaces and continuous transformations for topology, Set for set theory, etc, etc... This is why they are called categories, as they categorize mathematics into the study of the things in various categories.

So what I'm saying is that I like Cat, which is the category of all categories, which is the same as saying that I like Category Theory. (It also sometimes, depending on your axioms, means that I like all of mathematics, which is also true.) Which is what I (redundantly) said in the text.

In other words, you probably didn't actually miss anything ;p

(P.S.: If you meant to ask why about <3 (so why I like it) rather than why about the Cat, I have badly misinterpreted your message.)

## Comments (1430)

Best*4 points [-]Hello!

I should have read this post before I started posting.

I'm here because figuring out how thinking works is something I am interested in doing. I'm a freshman student in mathematics somewhere on planet Earth, but I know an unpredictable amount of mathematics beyond what I am supposed to. Particularly category theory. <3

Cat. Terrible at it for now though.I hope I can say things which are mostly interesting and mostly not wrong, but my posting record already contains a certain number of errors in reasoning...

(Slightly belated) welcome!

Can you explain this bit?

As dlthomas says,

Catis the category of all (small) categories. (The small is there in certain (common (?)) axiomatizations only, in whichCATis the quasi-category of all categories.) In abjectly terrible metaphor, a category can be taken as a mathematical structure which represents a particular field of mathematics. So you have things likeGrp, the category of groups and group homomorphisms, for group theory,Top, which contains topological spaces and continuous transformations for topology,Setfor set theory, etc, etc... This is why they are called categories, as they categorize mathematics into the study of the things in various categories.So what I'm saying is that I like

Cat, which is the category of all categories, which is the same as saying that I like Category Theory. (It also sometimes, depending on your axioms, means that I like all of mathematics, which is also true.) Which is what I (redundantly) said in the text.In other words, you probably didn't actually miss anything ;p

(P.S.: If you meant to ask why about <3 (so why I like it) rather than why about the

Cat, I have badly misinterpreted your message.)Thank you, that helps.

"The category Cat consists of all small categories, with functors between them as morphisms."