Q: Are these sentences correct? (1) “My articles are organized into categories.” (2) “My articles are organized by category.” I’m sure the first is. I think the second is too, but I don’t know why “category” is singular, since I assume there are multiple categories.
A: We’d use “in” for your first example. We think it’s more idiomatic in a passive construction, though not necessarily more correct: “My articles are organized in categories.”
But we’d prefer “into” with an active construction: “I organized my articles into categories.” Why? Perhaps because “into” expresses movement or action, and has since Anglo-Saxon times.
As for your second example (“My articles are organized by category”), we’d leave it as is. Why “category” when there are likely multiple categories?
When the preposition “by” is used in the sense of traveling, paying, communicating, organizing, and so on, it’s generally followed by a mass (or non-count) noun, one that’s always singular in form and doesn’t have an indefinite article or a number as a modifier.
Here are a few examples: “Did you get there by train?” … “She paid by check” … “I’ll send them by email” … “He lined up the class by size.”
Of course nouns like those (“train,” “email,” “check,” and “size”) can be used in other situations as count nouns—nouns that can be singular or plural: “I sent you an email explaining that the two checks were in the mail.”