Categories in Chinese literature - Original terms
since your book is an introduction, i would suggest that the "four main categories" is 經﹒史﹒子﹒集; in sequence:

classics - 經

history - 史

masters - 子

collections of belle lettres - 集

the long explanation: in 漢 dynasty, texts were divided into 6 categories, according to the 七略 (~bc 5):

六藝略﹒諸子略﹒詩賦略﹒兵書略﹒數術略﹒方技略

https://zh.wikipedia.org/wiki/七略

later, in 西晉 (265 - 316), 荀勖 changed the six categories to four, in sequence:

甲部 - 經書
乙部 - 子書 ( masters is the second category)
丙部 - 史書 ( history is the third category)
丁部 - 詩賦


afterward, in 東晉 (317 - 420), "~fourth century", 李充 rearranged the categories to 

甲部 - 五經
乙部 - 史記 ( history is the second category)
丙部 - 諸子 ( masters is the third category)
丁部 - 詩賦


https://zh.wikipedia.org/wiki/四部分類法

that, the sequence of 經﹒史﹒子﹒集 is unchanged, till today. next, imo, 詩賦 matched "belle lettres" more than 集, in the last category "collections of belle lettres"

you side note about the fourth category, you want to know the contents of it in which dynasty?

edited.

ok, the internet archive has the book 補晉書藝文志, which was compiled in 清 dynasty. in 卷四﹒丁部集錄 listed all texts / books / publications at that time (from ~p42 of pdf file). you may glimpse what was included in this "fourth category", in 晉 dynasty (265 - 420).

have fun :)

ps: just curious, may i ask, why you learn chinese literary, or it's history in english?