I hesitate to nitpick on you given your surname, but I haven't seen 中文 (or any other _文) referring to culture specifically, as opposed to language.
My understanding is that 文 (in this context) refers to the written language, whereas 語 and 語言 refers to the spoken language. Which is why we say 寫中文 instead of 寫中語. 語 and 文 often gets mixed up, but the nitty-picky-correct way should be what I described.
FWIW here in Hong Kong we have a term "兩文三語" which means two written (Chinese and English) and three spoken languages (Cantonese, Mandarin and English).
My understanding is that 文 (in this context) refers to the written language, whereas 語 and 語言 refers to the spoken language. Which is why we say 寫中文 instead of 寫中語. 語 and 文 often gets mixed up, but the nitty-picky-correct way should be what I described.
FWIW here in Hong Kong we have a term "兩文三語" which means two written (Chinese and English) and three spoken languages (Cantonese, Mandarin and English).