Symbols in math come cheap. Many different books and papers use different symbology for the same idea. Is why a lot of math books have a list at the outset for agreement on what symbol would stand for what idea.
On the other hand, you cannot use non-standard symbols to represent a sound in English. For example, nobody reading an English text will pronounce the letter "k" as "d" whereas mathematicians might do something like that, but they'll let you know in the opening pages of their book.
From what little I scrolled, I didn't see any category theory. Just some elementary group theory, point-set topology, real analysis, linear algebra etc Most of it standard material for undergrad math majors.
> And stuff that used to be simple algebra is now explained as something like 'Abelian group linear transformations'.
"Simple algebra" means different things in different professions? For example, Dummit&Foote's Abstract Algebra[0] would be considered "elementary algebra" by most mathematicians. For another example, Principles of Mathematical Analysis by Walter Rudin[1] is "elementary analysis".
On the other hand, you cannot use non-standard symbols to represent a sound in English. For example, nobody reading an English text will pronounce the letter "k" as "d" whereas mathematicians might do something like that, but they'll let you know in the opening pages of their book.