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.)
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.)
Thank you, that helps.